TopCoder Statistics - Problem Statement

Problem Statement

Teja and Raja are experienced players in CSGo (Catch the Strawberry and go). CSGo is a two-player game consisting of n rounds. Teja and Raja play alternate rounds, Teja goes first. (Thus, Teja plays rounds 1, 3, 5, ..., while Raja plays rounds 2, 4, 6, ...)

At the beginning of the entire game Teja and Raja each have zero strawberries. In each round of CSGo, the active player can gain between 0 and 2*k strawberries. The actual number of strawberries gained is a random event (more details below) and all these random events are mutually independent.

You are given the int[]s A and B. For each valid index i, let pA(i) = A[i] / sum(A) and let pB(i) = B[i] / sum(B). The value pA(i) is the probability that Teja gains exactly i strawberries in any one round in which he is the active player. The value pB(i) is the same for Raja.

For spectators a game of CSGo is competitive if the absolute difference between the number of Teja's and the number of Raja's strawberries never exceeds k. (I.e., after each round the difference must be k or less.)

What is the probability with which the game between Teja and Raja will be competitive? It can be shown that the answer is always rational. Let X/Y be the answer in reduced form. Let Z = Y^(-1) be the inverse element to Y when computing modulo 10^9 + 7. Compute and return the value (X*Z) modulo 10^9 + 7.

Definition

Class:: Strawberry
Method:: competitive
Parameters:: int, int, int[], int[]
Returns:: int
Method signature:: int competitive(int n, int k, int[] A, int[] B)
(be sure your method is public)

Notes

The inverse element to Y when computing modulo 10^9 + 7 is the only Z in the range [0, 10^9 + 6] such that Y*Z = 1 (modulo 10^9 + 7).
You may assume that the answer is always well-defined: the probability is always a fraction X/Y such that Y has a unique inverse element.

Constraints

n will be between 1 and 100 inclusive.
k will be between 1 and 100 inclusive.
A and B will each contain exactly 2*k+1 elements.
Each element of A and B will be between 0 and 10^9+6 inclusive.
The sum of A will not be a multiple of 10^9+7.
The sum of B will not be a multiple of 10^9+7.

Examples

93

94

{173942897,55729246,750210935,595502724,350348365,592823762,458608170,776609607,323119032,864461632,165070684,666663579,429413850,333023455,112574938,347731663,557777257,738042994,693722695,2719749,605771991,18997856,749399130,401673939,74036497,438933225,358577447,530058107,803270320,34430037,523882664,929880014,242088164,143230750,697948459,207049279,466520880,558223175,783862665,806815771,666489889,696364740,465146765,405115507,938856081,112734229,487776589,641992937,819233701,901747810,546641883,374758559,300585567,535158246,590693446,190747630,384909074,109251910,635232134,257068012,104154975,415569231,779157254,344225015,237766507,801230930,203833175,778264398,894715915,291637259,823344262,150395447,609202957,329898585,464631001,49262862,845687681,635416409,426098733,433857275,644347826,319809695,327864703,530067695,199854302,255773760,297356910,622339043,642076151,870539705,915730076,590967687,878656138,524971841,278882060,133050745,745149412,637523040,341972559,411913209,378921911,640622952,729317555,185850611,357656169,378102175,605874302,12830617,463934327,116054463,597027297,727759045,715559460,839045875,580649244,55850006,865638857,31915634,774560485,45908871,60222101,533242219,424685930,309871012,631134556,864747367,611132340,364054686,111732513,356582513,672080192,232427764,335555867,957709682,340124444,581235568,792058264,857523148,271111060,136112775,247942478,242830789,234779451,957413578,303999888,93151839,313704174,975913056,537056351,857724047,631758051,514899396,24007389,861327739,467762210,983619972,494690712,73367747,901656616,643100798,126338601,467625875,938384393,781372265,924144063,379709907,421529312,297113493,557566374,648980051,330006808,204025155,713703072,871588612,844961568,953909301,774177994,484270762,940694463,147410464,120203445,978056997,803306521,764591367,932657562,968590348,32452512,87340316,961610932}

{244517388,539082635,940119719,238252597,414426282,83735537,543016877,493053949,679145355,891620896,587430590,132327304,957195317,43894524,293619003,362617675,347630186,566961558,100142228,659236937,606124483,711530949,554234989,356313025,586183291,5176493,28361751,380994623,21806217,629623227,397570812,757497487,43391477,54628732,397847046,205809485,53387255,505972343,757857601,133336687,787782754,83251176,800675049,860948548,228840200,252094529,637609667,500633680,320543279,273541758,310652143,184842142,200873468,403456424,704511324,326222272,481373890,923139298,139571539,529232468,153560063,658122435,439460866,37931817,428436953,988448475,510686639,120957679,629433730,43876327,173290457,741744834,782937469,617618894,451433290,702475417,909347012,840354330,89867946,724043763,293338722,731851544,162401344,591089544,27937591,778859924,730762271,219461430,467601899,872042267,496219135,662907022,798501034,981484510,508662595,263949555,295030263,580663357,186870552,227364258,739667479,760682991,996072531,141539668,284247507,154167574,738445482,92577828,984053199,415509323,816763209,312017883,968144946,34035014,279599775,476715901,96344671,266114267,158021138,41111324,838190917,287882546,120859110,728277822,345480514,831339773,970284217,789436075,542456744,845446508,728660980,127765705,273639471,22256006,344533659,473336836,542349623,739510584,205279316,896697177,656207984,352746516,159911437,300157397,601611518,498040915,432219973,845430250,856363332,78393893,787211163,444215043,564677801,430241790,860531926,142324135,627852263,498455499,527974888,840011709,124221781,369904388,806339001,54189200,536205176,699534123,194802048,200367226,539119111,355957630,628273128,564716258,271272197,237993311,855531156,317190673,498570903,13661182,378465538,162667935,82804420,633797488,77249878,306161466,86439914,769104487,769897383,586919935,781367049}

Returns: 301673145
91

95

{550314539,475160590,327327139,61824143,111046829,713632911,997547636,366434031,732801840,364200115,419681528,769693399,953810034,600178119,211481402,246183452,160613368,812985600,508387078,470050158,724351786,87278033,42933761,623445765,454229659,77535500,748686448,670274738,644883004,141895673,710152500,642585913,165502267,911816453,586292456,351540258,952520011,550634968,821642141,821571178,953802314,297392026,72412521,473316656,803146685,706921545,410422511,895645318,263708744,460703,728930036,255109446,905264330,764307077,287345434,711573195,425903248,962430209,273268434,185365262,472209296,835926503,962748858,257918790,519676135,656154818,609683158,434060461,892079139,200237523,534198012,228698597,396488490,678441343,280336217,539147919,732403416,41925789,11247649,823312418,249130206,527883043,550773755,94386328,580593740,928611798,115372754,224500458,262467847,14917367,472281638,763817637,388440716,796482008,29539281,573088200,357990292,479427017,876738884,107535721,831055175,215817144,636559029,477158891,599730509,507279153,139383153,446491004,208444248,514171517,55805586,406342105,112161382,361127948,946466218,899845171,823008386,76776104,776333795,328767378,891886574,1346824,482408011,496784953,121426907,576615594,263654736,284841244,948367248,182145899,868576537,15319242,233358038,321098910,691581517,911266522,185218760,835928382,579418089,761956204,165745189,876197149,96024520,893905044,528848066,860097289,629191320,396297480,622751619,94635723,622352680,186511988,209538300,297808594,810371253,676701297,860328195,563997817,962207408,844452816,613061309,574772802,831042731,583344034,834667858,550572728,688308719,923238197,442043092,953366814,558181580,757754269,96705254,639229833,827670973,221969527,391762902,449781555,605366841,15191436,986214453,666367049,870263423,466057292,698599849,310582737,192099564,156658489,946382258,783226882,590896327}

{16713430,860954399,489300502,412273419,69523814,75269798,610381809,963956338,574341718,704719350,877432893,413336142,323562628,881895243,437484006,909838887,41201007,927378070,580829176,189979853,441043996,560883262,26767216,445463455,822632869,550945134,169392943,374957368,132795232,43252167,919403339,574601845,532384855,910602366,474359678,111578292,235345800,875649649,429958121,473008003,539240029,462404734,276798447,515677980,532009699,728188600,46028491,646616289,608369097,203918763,123176233,153289436,119251208,533266490,547435810,659331470,908189415,160427321,732125404,518854601,351655735,788813597,581614083,337433753,878934933,964757533,973282285,892473079,511850202,1867017,720598161,793607952,708326398,80332575,499478716,812748295,319042968,147179418,520909667,620994267,731152680,754198921,281132618,85756023,330085532,345244744,483750308,378861373,300425533,679787455,401708476,41708533,23526785,646346877,770699562,461929637,328850401,794597502,871068493,2300677,527433478,52829642,131585136,369491724,201070888,436608640,504489971,862745044,310041142,264874333,620907560,989391323,145060533,100046669,895451974,149311033,164231176,140843635,332440410,162182377,428651949,69299942,880357977,236338609,207707396,696954109,292603996,653501669,614281115,136532414,88118477,478402665,478030886,974592155,34523267,307088051,320337464,640477810,760424879,4535531,839052865,73973149,133111969,348381084,803037917,824042535,481305753,747070232,804339,337640905,386993933,773313458,56596445,444300060,886366800,734867596,980276262,757188139,997296212,786360265,52895330,903359192,992402578,641094310,231409456,973722853,472217356,671554035,438764408,158974709,56517976,834759242,583479974,90405543,196700857,543591967,396265911,930039596,878235686,656291028,18758786,708398079,696286946,897356799,928021906,607226206,980053365,383484073,421297316,577438159,100546420}

Returns: 834658206
99

95

{109060775,553017286,616384029,703371393,253408869,84615516,415749130,392357159,270879544,651366604,816041006,557262912,947309039,937970859,258882008,25503913,199294727,127338624,567413273,962654268,789982790,798592689,92938528,697866661,282159472,624250984,710626819,524136132,850713786,412838184,236683628,994973826,476601417,401944135,698965347,417012174,282943935,842321378,349206629,676967991,491522588,456200030,624263805,258863897,553288812,61022731,100591798,468653449,943422612,735410794,123694570,428185626,216159367,30340405,994884045,384609645,188577511,296562709,13235938,504363102,527995189,277816321,748537709,499878319,414447065,697068961,498233172,526389018,254569969,65694405,912514260,312616449,551837469,317446818,489724954,579279686,95008235,297970774,965135432,982370284,135984761,281421994,983868979,349517119,733487080,255366445,859745160,674957369,0,216990785,140343545,927298578,230225662,613727313,601910164,398669073,951547927,739817252,652586204,467285263,801288568,303758153,60578511,157115309,304343071,323533478,783896550,402271259,134009560,778984606,981487200,632524847,307105633,681864236,618830730,627407534,220676228,66290876,129413198,477267796,522998656,592432915,847618678,868460332,866639787,235037912,113637404,7821906,567456725,294158194,553960902,577150484,420781967,434697347,391782450,641124804,595992522,65359735,363072654,0,432186207,398813475,694778799,530577767,870439704,100486577,46243111,609652980,27521757,112296863,822944714,875703370,439738051,460638720,572334433,995930702,611762143,813120,583920881,692375393,481214988,929680812,938079397,689239697,148628326,392054790,568674213,699735558,400768664,253304595,20259067,273822045,874191436,177656660,130408761,478984821,934167060,78691653,192794790,478122919,539229604,123259438,886705555,612002443,943956276,820379670,488660440,194035192,776614333,476139306,970816107}

{312382093,447873016,999767659,758005343,705541753,289514090,54581605,180946672,755363102,307262546,335124236,82266534,260883044,652916850,240337264,406507693,124999127,962034009,288973394,77460632,848625468,561885176,746224869,412497523,262746306,693861663,564233860,693403212,298712949,325519019,687929580,214961039,103068623,552503187,109325663,803208407,171120849,504263318,69898004,333114481,272610165,639086411,968239200,628679070,46307489,96215271,716336058,410132414,722856014,194954198,987770712,15959525,201558526,359871428,186517132,713317316,236314385,473612583,532538194,78511210,258277354,678899117,426962987,16696255,122313538,212326278,443130564,846861881,699663643,31063780,238944302,430650757,57576659,792007487,403519490,286795691,21900875,224081359,435450752,188397621,299301974,214468703,810302959,483437608,305782400,594539785,387724902,365021022,854474445,141439883,941335029,99852865,443948971,525849861,676331365,478406531,153803237,666511604,14258907,930497000,534470151,358948045,609326016,298082248,320754987,614828929,86775831,214297616,1721637,921135912,416835242,181598943,329210469,949355598,516201626,275010711,421034106,653665724,158915896,980744744,387367616,805701071,49360295,52782490,491298637,55541556,111623413,140923462,172595826,332486653,660971728,585176806,698805447,402544688,617477359,8081549,802913538,205175086,877674755,39344823,687378636,748817376,420828819,911718695,905187918,633473138,738122118,511756044,482738563,881178768,676398787,465618265,637923982,602029420,88919502,976987772,14050478,122363062,975841292,438828114,54179374,129974163,218821820,1027696,710926102,582391625,255825191,675450168,769283911,34382803,352053420,595953107,337261288,75279281,237373454,809437641,90457455,748285008,340308327,647225406,777429303,191323165,272342486,368568383,555736077,304991468,219378788,375441368,507989699,247018843,93124291}

Returns: 968432635
92

98

{530934066,886232704,853762360,945879137,4667126,989436150,930868500,65092476,604423280,199445361,946846843,282862532,136673391,797346887,473128460,147712409,124453810,147680908,942549546,166737834,323700752,221713704,954785223,0,282191931,934191830,49506049,820672493,453371326,988544620,962367066,121445969,252804459,763171723,219862186,146005422,282173290,629615896,815301644,601007303,994555579,351342466,174473714,157265113,432403412,717302891,584741337,589029080,397877462,559840286,482012529,319296589,693894450,0,359821293,997088386,144064916,431328923,348366892,91087964,786144749,268877439,992373891,753770490,14254880,19188005,53201379,134313457,688946604,83566718,233482456,638616208,99433530,512481777,156348057,491921116,524784811,138779147,820013439,598370740,85254816,412424350,456857041,439336491,136130334,820626284,301540423,42814442,184109207,63174018,944726088,632266792,497600244,638790050,366037953,843486707,894730471,304950826,628398296,197715597,432048708,163739524,279523830,668718411,372290093,154863379,888148999,816525852,585632342,298365981,442514884,894438027,991109535,350161495,588763402,301347953,186940644,127691379,366120562,409088077,521524340,577204475,785178104,71427918,878361007,818466752,304602294,53075209,409331774,581129232,723174086,967958755,755210268,512153390,311244957,455485952,950075774,127294175,638114573,391644885,541699286,447507830,704198976,816948055,800928689,638076380,953522009,888028407,69754918,186209797,612916734,701886051,96420798,85138163,109877841,493184120,717662093,680011218,678461277,94084569,219040775,869027418,154859679,566604171,545120037,378807083,807685600,857890610,872817280,299059722,845169052,20529977,796136751,731165682,652202904,443788590,529108930,83682954,807612523,364499047,775035657,174130350,791171071,369051536,717405216,489709927,0,537960606,996493671,761879870,853540483,656099958,508911224,801723037,674105292,194194131,213343991}

{873406307,817396636,674089477,467626865,623677772,410015295,689427773,798899923,470015848,357742437,487751338,403582741,970831045,699557064,270519720,638518546,183457537,310999403,141348827,849471025,543464436,223944010,923436835,229484782,0,587122134,444061077,509989826,833375489,82432639,756037775,773933510,540276855,411217680,276018911,624778719,660149534,885366782,292014526,324318145,287296807,207993799,779990145,260919925,839479818,122215379,395662217,5203152,653251858,936241161,229870380,380803320,11674830,108045097,537484709,346142918,322201153,207951622,408679898,895395337,489883537,822905515,262954886,723645393,271053335,471214942,130387944,133298982,623356517,119355297,341327581,797432796,272619597,817322792,775913056,962283011,39598410,538236120,499454431,921383084,919798559,928149642,377928405,860629558,849714306,113431709,326875334,152086235,587511940,928104685,294938946,717938332,8318530,218511203,143759067,660670736,123682234,510825499,215227121,440987374,279585209,601035659,384185630,400087840,252137587,251773395,799309284,347843084,808694449,306254451,761821441,297594859,777616858,970368475,315292391,104777647,32715641,876678115,504296136,246692062,795030110,219452963,312000905,823801685,548526873,721905500,139465538,182378273,712727523,843548754,991746938,317424489,762947981,44880544,598170882,842876994,786090653,801877073,946575167,0,952705890,10677552,402279708,515031527,988853710,537353205,974902230,534567524,731392484,276883947,930853821,438605663,780651941,149040538,424267509,433199374,410814582,469798261,328725550,132591805,222113621,839081650,703753084,976452780,465541939,967528638,777421693,794470024,270325589,807798218,925204463,135634636,835334460,132063190,496001106,421320211,686098502,629844228,776716478,413024994,513577626,135520242,688936070,566328575,129716264,767123007,690032624,622740011,800160957,97551412,157830485,516859505,794112082,51993749,486911120,897611905,787175164}

Returns: 199520048
100

91

{682129336,104967788,602250103,179103762,785067008,476226293,803910275,44418881,378027591,570750179,938465459,643664262,767922068,854825845,513616680,877585761,290420724,130017236,287211141,408498817,42743788,425179126,548486813,717712843,261930398,796224340,881002215,202676692,240936957,415551753,392153507,835618827,598981388,817781895,962416102,320933723,349199901,711644719,947309039,122547800,802084465,639601423,673461872,447015959,778360781,980320106,751867885,817761758,323394748,408415363,114192429,307186319,630950475,410920882,622937334,18502701,666432444,955729262,258218985,905344932,462087208,341755820,788567003,974413775,429201827,257976336,725507023,779332947,351914144,235611015,343577624,868390558,611598886,798858015,383191011,380477233,104440892,701753907,917442510,450906233,158189277,85686864,147816452,627319480,874131222,775438595,297287237,697252992,368424429,209655170,339001712,665833209,178511341,463141479,42477485,621754142,993693947,542479792,26239854,118627032,950544193,904766150,42790545,439460008,373360776,250773612,516678692,407561234,50255899,653600483,360513171,932984690,249076158,631058174,608058670,727314123,134599601,163111180,546866559,770552485,746693788,247290114,258336593,737931851,494734955,993862980,247897607,54033973,403956639,786032540,214859635,11215032,971364350,422826447,589590438,999531456,809040334,486047444,339965763,264368035,211623060,723277666,935210891,867075661,740083541,562409836,201845021,360756938,22630260,812676369,838395729,175019238,534849849,849412528,750667905,381939500,841903598,340512414,349919769,156712952,821452782,549786322,265753345,763078303,443061121,112552485,982682831,454712,877943628,292763002,918589293,192838004,521209268,497509102,451482858,713253652,299667280,626224287,136265494,763227875,973348713,111494672,219645261}

{98447027,958105300,134864070,100041397,851342528,148958336,620594908,33935990,310646065,844659818,3794351,916989802,358992281,597182206,353264553,569809269,349422660,657614899,718471856,758004743,30172787,498592987,857766124,992401251,722757625,722080107,680909506,125424440,148827225,781085941,295594239,955926004,624063662,808189922,500851695,618783130,988461829,274309050,19404963,622480375,4996263,394715928,720846025,850825804,571261162,455515314,377361193,13137210,431464055,971304898,954886108,870328037,734021754,718527498,577205680,242422851,695754732,685677642,115973187,782106341,730946280,215162465,885456669,185619214,32331813,912626227,543781164,323956278,878359946,962448890,752358416,763259722,389227709,445725633,183640195,81511931,182661737,583534713,847759042,920031027,300910606,980279696,493649584,344263102,656247432,187907941,613845918,294680186,760185876,746539470,269280949,273131460,273268098,58838447,148980077,923723236,769112026,934606914,138972029,998321101,275080101,972211725,472836752,693465030,152879508,496186733,657129511,151385994,718762183,912072704,845324129,107633592,759397384,572479719,975592667,643172909,308550101,889450899,783288023,90914359,77536056,483766031,577620105,392994719,109096164,512378988,816260199,260243647,248086742,387544170,383634333,849216709,269516875,162793954,901554876,28659420,475116448,5023153,74829536,452780543,529408571,27702484,19471758,97013874,95905447,62569372,53748051,74610469,800146634,379618844,448941380,810817838,821033334,668106170,267905205,259750972,945843502,619312426,269973328,958920466,472160712,993278949,427563520,767874623,422991813,516700946,503606884,904893524,964070541,127489673,455722066,179020922,770314060,861958661,212395660,726418380,184240614,546853586,174595399,565192970,148452610,37646449,635445034}

Returns: 377935165
97

100

{677759798,778754242,871782623,131803256,713499819,478205565,933573185,93552199,525381688,8073407,885348647,834013546,857450436,946881109,205849244,360208856,215970990,567999581,722442555,226020523,397269905,497483302,849558155,233316707,948910886,59633748,114354215,557542374,269843068,709560895,998180775,350520791,416857100,511081974,542708235,999575157,880426719,300032379,905251965,240473547,296031155,641412994,785662665,806412013,919943693,281014276,972067834,317606708,407810797,973297178,839712549,812069215,634890662,2404800,356949754,673784284,227285280,766521347,637716669,550029096,525873124,128260932,86211928,517728358,373514191,440047405,658114779,939337470,471492926,781369733,82955667,646052363,358481637,265629274,686193425,98545699,212232217,107574975,196067280,575739045,561156032,502229003,604331639,920161206,781822018,584923720,535572490,78232687,296115989,893161664,596486226,660843267,14233180,475911328,109511643,821614392,85135879,210042034,91462366,861455677,577583383,127617196,442733490,979396354,904804472,194000948,105070907,137445529,5008589,968772048,297415842,348425274,635108609,471454103,781445803,243500369,870798032,790184891,713870214,453943948,116942876,443609929,999925680,743299939,560614562,693437565,270790403,563081908,367587053,135327692,951144059,533283090,893225586,21357413,794388823,651783653,14806445,117781906,976868043,171361770,139456451,605875631,343586865,545377387,87319067,678040230,191739043,570129073,361455576,583621851,691431059,629326096,255324400,189612198,343717232,313561451,229965496,186760947,757535263,360982387,66700472,806275164,443317770,485103687,71103970,117532335,425762998,597474328,562956790,454197049,273006509,195258214,95031903,367639233,779602457,474764280,791289553,310485260,523136908,430497337,18590012,638612018,939379400,668382335,193014777,193279581,412836279,693358980,585853051,349377029,189461913,329584321,893169801,624388620,557058556,964486413,252162220,992944721,112852408,841125055,364114852}

{942397102,213095321,921576766,900814093,244568211,574862117,820027837,677556980,61500441,643500178,970074003,235062943,428319904,817800753,64132532,452032649,843442635,49266579,802185544,86463866,401820074,742634702,1956935,528302147,234345501,332677384,641753611,724181189,772232380,553611056,860536866,582851186,20170514,407049421,591757356,378239041,804913701,606835168,674086072,753080722,861953183,47591597,89858172,561357936,906836521,87912289,298967351,748906609,391319507,715717208,600483859,226325120,75051500,985255970,189733338,683435229,773951459,487489675,17462178,845764419,191289286,421374770,327806332,392898929,78010586,583344034,653108565,910082895,140231397,6320811,76464741,77126250,208021162,482609001,408272168,198290472,911346066,266320988,668132841,764596449,458980201,661001928,935211336,722184307,476681868,845954290,342244424,390854868,800888690,299178978,790178363,782362672,521352128,76784548,862739083,658642496,744079112,865142209,805689034,567646200,512072775,84379521,648769769,151721064,405473297,800081098,538080851,530097575,870086378,737012452,91513973,826286875,682255178,961857130,925960645,127117820,29584756,282662521,728366381,145912137,224937567,943775908,848242628,264302974,286605508,456334726,801738762,34514582,740866713,481297653,592311357,779723608,17517170,96571966,130692515,876139304,914408315,146868188,235106899,983355870,975606784,135626516,717871551,711939715,388948802,810930539,845403092,58823398,440895097,572021885,674436322,275605579,730691307,939442874,694969480,56388267,359349883,172851559,170571189,542162591,482715906,947332911,93533030,708893269,100030462,83384039,276678209,492086360,157792553,19206707,584398857,806756911,326635667,60526337,734081811,595419739,742722838,504219454,131915235,570244351,302846566,464795860,470343170,585068155,488004749,277516456,907474094,279790288,646995567,169405459,239808630,631371444,203188650,370647050,382619215,792314426,887136600,691134366,401000265,17340379,352186070}

Returns: 134316488
95

99

{64396659,426373209,699782704,331157118,696328834,480458894,627794177,758635551,766187736,12881219,807056217,31790523,657231699,842667341,513764469,846590817,49495676,89080717,339779201,288840127,990949624,330070711,274703863,684085169,891289468,460783150,77827264,934497510,497304619,203593453,356147229,700576708,132084249,459799068,465423866,572234905,883744242,114110205,279958836,78089604,546848689,900001006,234857362,491726803,876634038,524997286,161401887,40440829,877354326,325180568,316289260,305702631,202483020,536736337,539842722,584126046,468960662,172635098,156125148,489387606,221914251,177832076,914534336,959590244,482240782,473520883,96562186,627088466,468880024,10634074,392297095,599173227,699978577,89380803,149623992,45673574,68764028,418702630,785338048,632698963,817092866,970590327,821741621,160675535,35497619,185708194,681039048,795584716,343794521,378300314,4636326,159361563,188965137,387072025,169312239,62832041,63423944,115492551,210173563,358764871,182943063,308738354,558940452,947466460,314931734,666892993,742845085,603222983,66782212,727578248,914431214,616479792,296905952,60831194,842411278,291146427,781356110,385996735,94197797,363493783,946261673,124762905,203801937,238279975,829766066,979220694,300467496,297062345,631675630,601373598,124954978,766346113,260675892,164447252,141691058,351412316,942800655,792312485,320977153,858792344,0,129086334,513073845,143035992,712378821,580506889,807274992,36803562,509086729,67817836,396098681,301836465,541217962,890146597,447323217,165093770,333458924,869574408,74729233,479513358,68444095,812704344,733806722,924033857,810207454,643265923,552396086,561648683,350665541,405580519,638749957,404386990,33209914,933186320,871466890,664669948,24404981,812126394,415959023,877526829,59367116,965791133,564994591,821486287,735727271,248769909,329097134,630750867,492512913,72796777,484517358,179624051,542004366,121470533,847339821,875270606,616834611,27302730,96485400}

{418709810,529014469,502363017,92053856,335114299,245189777,368352154,849600856,487732925,615067160,351673313,713811987,694570618,732863499,993246079,265724987,637627240,286147577,296688747,129818599,943963010,282713999,82117005,481374431,412305510,826897807,737148618,477798829,588588253,684609156,930930135,368255245,957716082,428176803,682948938,704871774,128663710,108263572,239040608,378964784,224453902,764751882,111454799,62951033,877106923,178152651,340848879,273279117,906382799,519016963,158017352,746302420,220816383,665586760,245537082,327436752,23780370,828752670,850174587,45329808,119973749,883981524,204582721,952796752,348324602,868999441,748625251,465122548,229759730,100330174,253119462,533739002,504795611,72959049,337885789,512684497,186112428,818739408,766352443,672896242,188031649,165484206,372782279,608666229,253342820,294184496,825887773,250565427,793821951,879557265,716262018,732142390,789981646,791586897,94684489,338210394,287749382,230065941,874059058,789354840,357161891,294716224,293374267,368621378,147843897,839632343,692640217,947919662,398348973,460731777,823132941,741367625,903661212,33677378,378852619,270330933,627946708,700951861,621240784,77012854,342387362,24707590,911756186,361094676,881988364,863089795,835634841,482827233,44100036,308216550,666509772,685776338,287681840,444426581,437742601,632180422,760276233,654093064,136576375,720520636,963911654,204158187,286048724,893553422,201085659,298316194,612516104,786041597,884148638,641060207,807063884,93614047,196429402,881162000,174494824,377753342,836262165,331519347,372832440,523056414,646998635,978067160,103010289,253851059,714085845,827362722,699805216,978602244,735921299,695501300,142938538,852457572,450705757,366381411,529848387,102306586,141222778,869399241,901340061,287569595,370136697,11009678,418684951,879023191,862634145,370151695,190085558,378980765,604160971,227888982,474647083,524404510,348534634,208691171,779112274,538547851,456570521,690186418,676996907}

Returns: 218509990
91

99

{700938514,101503254,435910865,994021128,538392801,495924499,598812869,26885215,438203233,967813354,763504839,16400180,86646807,551347257,281354530,64715313,587971893,65405380,284423722,846836857,442734300,369378324,78703140,716791112,382632501,818449740,767501221,137761399,729053482,755553879,437796474,486821115,700979785,998961475,959595709,784653338,479633728,236149080,507198118,625630728,886099503,295074312,818981185,78861899,854931610,175529208,981062338,314316444,970024420,134838147,506746465,262496448,759091461,284143681,884385192,282366853,633937444,740554224,157684463,891697960,870931947,461999859,556441080,285120690,264304200,63413493,793018730,375066648,624227801,81918023,313081876,345266605,768310062,979772694,111175384,32087539,544546543,998130406,290171281,566576116,390424620,608836390,683463695,731264623,877979000,384650439,185515022,35414727,619365996,904637112,559840346,832276302,793050160,247117178,785505775,557928045,419492510,445811871,907399978,138542829,423250086,403991451,540911106,123030830,735429618,628648764,166739092,622885867,441423901,180384776,783776882,384413698,828484432,266298297,379993153,793896699,501394561,295074916,898967593,913608798,896886847,994569885,125802197,672838501,325599257,505175479,701002859,299482413,566401921,715123515,865279312,291679201,328463871,154921354,361686225,641035934,333860251,636399282,183175633,471970644,641253009,973748372,104328025,443236477,427099579,93772940,984873869,985348620,337233306,329714797,879705270,94715358,858214001,902762772,970096913,513950218,548048305,12414462,232412581,554848337,650497963,279352925,66194366,312669342,478903072,711764669,382458965,140348509,238274080,367457658,604560909,669661081,631507894,294815169,203380660,408288849,833386881,924945502,449253866,128030836,748502258,544234609,521474363,756547196,590165187,209478011,118598140,559483558,976711608,287775956,883134243,452577973,651431716,404162640,368884467,977582969,198052960,628321277,129297747}

{919257184,252804372,47283131,188877797,791863978,743589995,669372922,435286907,394197885,789879153,825771046,680167035,66983781,963977643,58355200,199006750,227097042,747170051,884551532,451057687,152497720,718207352,294213416,543480197,371542705,21075125,822358314,907518918,989902878,210477478,169015304,0,353831956,216944226,719556604,655078088,110710756,403457683,153368547,202861523,386324254,155558050,250495300,650246935,136725639,883907390,218193235,241528073,317139470,323468287,735376086,117967984,539477789,825992674,772624900,800666649,576099396,807479305,374869543,873567889,903647462,177998070,176026258,525273076,398698284,93713560,772537402,768143349,831802165,788305977,18866409,927322795,523782014,266898846,439911579,257789923,477182919,657274094,26269408,230472798,604511900,329500359,899482274,301415804,360450994,500974201,797312365,739395510,266642964,119216482,838133377,145344673,591434317,236985628,479579155,905885070,904149629,533887822,452746259,848982029,956647768,386504658,531582380,108917292,670021301,300360133,232403092,222593787,521439420,72510934,559874721,408731319,855510246,363270213,977359105,513937281,943457464,782362514,196569981,157866469,335008694,126342156,801723037,228439904,611573213,462330641,441314702,890982448,26670866,807980511,828365917,66730546,575872459,72887412,69534154,418607831,779789287,154190169,938276976,344863828,999333605,207815030,928566482,178008263,198566280,91024753,322118541,542309051,348482706,89265989,897558582,279326595,436993377,436268272,195673626,540599787,362073160,356828762,92020597,20050623,678870585,519194947,801499649,221653671,197493640,167188133,572558417,262474760,609093454,289060541,435400024,275076288,906657048,892353199,550370308,987315365,986093563,27124868,503146273,284938811,69393512,262834499,613570916,858719030,427873687,571114003,527895284,912724681,231781012,723289113,773211939,267953272,968291584,3388990,840988613,144993484,306835805,14104698,975250413}

Returns: 664232898
99

97

{452191774,448545444,765704850,410193159,361063808,305299519,232869858,855369351,644387865,74024276,917285478,414636736,495708873,523010512,946424751,0,35255903,0,221673554,971554186,141197753,155805136,150186447,633155297,699644695,616255922,755056495,938749189,829112000,976593520,427149925,840210408,190413854,395969205,893480488,560446605,655440350,478688900,318813857,334219114,616569272,693405756,525770698,168414056,272846782,718524309,499430337,525902103,669678148,233382922,284846250,198460687,558455646,425726519,587922505,132233542,338226068,535355399,594522110,378662704,929552438,498748900,97231658,636269369,803656936,924603828,656004551,266820222,241905259,941400972,656555593,341163121,443262776,109991324,363850121,836557193,968074778,352861755,567378918,983024838,132083817,402498241,204486306,692876529,198175747,612747714,860650219,499887757,384595310,714488321,176970619,572509572,296555578,165962518,574854264,699676390,664459196,770615273,51581250,451427315,55685443,565669179,81320522,455889365,373270573,94161356,306961869,577257122,822291749,771877787,142910617,367144007,226532360,981290747,946723001,409580459,591994569,434451552,297942842,9368910,672009714,776748708,200172473,866399530,10912385,619286069,959025858,786191913,745374326,245194288,343877785,681379074,464822733,697508773,395139364,41624774,472724846,533031047,660418142,139581172,558002314,289612371,916280006,506689954,944912215,887002999,291237483,182858593,463474090,834091190,302850471,515368216,955446025,285843925,722402895,849818558,906679939,815521953,453527457,601872229,180447414,473056124,860257317,31091594,608463914,438758753,303248031,835372442,527099350,950338358,109819344,469911045,482309450,404116487,495917872,719024118,127717976,581716936,178357259,0,770839464,759493422,873352175,995528873,547812303,868012364,60620911,632922363,188901525,156584281,453473900,288031847,750298013,567577110,415882685}

{197234030,842940750,255801852,661175421,767221056,388304187,517602876,344614362,985211264,847038751,245722209,846827464,37036869,123521192,547167696,486230111,370830152,34793105,588344250,503984509,767741997,998514895,737360424,817262245,576621719,780161270,499648992,39671838,393294267,598334777,435031764,566613853,69965072,875632224,264044071,797839893,488497594,670575622,330222497,445709926,462950135,229510941,742977527,872526000,264004347,949024699,590600925,77535712,287443741,378099121,759103413,11661859,418916701,475918614,952391105,45978034,507965228,134156248,725556254,241796279,964344496,395464144,719764412,163786662,265466544,392162885,123932571,669294708,381736726,313233702,652300228,9220848,633602843,629575783,680972562,507640461,126125939,825847067,374081711,399400862,50859667,953366326,24506847,648426279,370773417,707561379,666626459,181062636,59600856,589737898,363621154,191806460,738953993,459885501,768682561,269731807,849956162,497640160,856706966,438456266,973050851,63679705,39035359,458734043,104970730,691727077,241478036,704123425,611505513,917661481,509417660,42198466,718972510,978372232,736668232,221875714,286540478,207735797,17328183,343096689,682190763,709232492,51845570,229956858,610102000,438419919,455089774,130054298,572911601,974219583,584297019,631177359,721966408,49159711,278300011,912810678,367739610,517746841,54982077,903359158,421766613,456405960,760078170,190912283,920542522,242444745,637796840,518883655,753128106,843929668,876202162,512881637,948130621,526861630,684278563,299323043,188450167,511899517,754862789,941697914,671837735,454634304,174320757,787864514,14763819,801387266,27345569,841774218,173027226,467780919,193217225,517715120,440665848,981402792,277376304,406662876,750925824,510637721,19513297,902878867,639854515,559801273,976473451,986572470,493335585,499514278,108541664,849915186,240366486,197239061,515768207,175708014,493032635,641312636,0}

Returns: 838631225
90

97

{360706916,566688341,260532339,407333352,300266161,861465771,9695541,63860599,313725838,332085925,609909960,840077582,116688730,484555872,435623062,143674052,800550230,878630147,432214813,45122937,681204624,558077569,933229020,387727978,403301794,522999622,391290828,170188832,340103775,336826908,952040956,195596542,680209489,997398650,31173309,510551033,901549064,492210028,605777306,75534398,958769817,673156738,76886658,336957491,60938934,119866994,54954890,202177665,559708530,476505663,589888458,686915338,796697462,418011703,248370,461552976,783044980,430050162,56961350,318099071,378217105,267711226,807463942,841773890,412899353,881360106,793309463,693446422,830140966,459675213,770656252,396428457,870347749,681151808,682870200,985979897,41100633,459387091,966878927,183666273,783239213,724204419,522447792,424137413,65561890,28293868,880236463,591043064,916657402,717552277,328796533,239061544,422515299,775313018,770977831,454040309,294583882,2797616,822391969,558229707,101812950,867337,982788188,174789799,751773054,817401552,734399985,611866150,358110492,502380982,312036508,176558749,967815715,748409452,755950319,33304042,741864482,69314826,800387755,91636456,761563107,564103960,691651580,294487880,281285378,457368725,484538732,260668725,831154893,866994334,796975415,1889521,678863050,720894358,280652247,427770296,251915511,4241924,469064743,55672691,462871900,778232255,608143109,479826613,584863207,114226795,582253503,302707334,539750824,122131517,319178878,816161528,903843167,466450970,245055546,993764083,569792535,703169834,233421384,203545339,327500293,17665964,7454110,538035575,610038447,821571473,517927347,741513480,941038744,883582597,202954635,133727012,13708800,367774370,9444651,323474368,840335040,874934880,342749110,651346584,432345473,540101574,583032256,789899466,366777944,797132970,987110085,401649188,449353435,530373291,473425329,255291932,130447540,685498000,801093249}

{905634475,572821418,138587794,600949609,117278632,637662012,807803263,509000081,712684015,687991081,763019348,812593862,967984064,242863765,328801878,898520767,722926467,703601893,744952641,297463849,459056320,107730312,550438297,956652236,131678757,392300480,62911790,632281511,928745601,784469567,49491335,400483083,363429098,404854554,747266090,991808187,59934983,41112404,726523385,402521852,323756227,893756848,53829554,693495120,146039549,154755450,408855323,704349454,396281211,288356448,86277143,164574917,276965802,625975434,918379068,105733808,246966849,475093553,391555672,0,897760364,270120282,730690014,275062751,902348900,798685648,952212435,643285924,979224018,644487978,405816084,557475075,469786986,729760721,19503651,239382984,307759332,6909154,574608086,552189417,343872816,951934502,216395967,96171216,460381826,25485190,179249673,278582685,251926803,156656380,249277717,878615758,457804337,740205214,733790573,980796541,168481308,680728325,447479547,469027310,719736993,364887387,997921723,114789653,123205984,369540503,312084748,578343430,893396222,896120286,60698241,604161292,117222507,510551033,724617019,971497778,763269038,531887717,650144374,999424983,20424460,888392571,745030717,27673348,116983038,843243001,201720027,707429767,53707628,3567878,636833685,83300395,64128746,319359652,137355354,259918276,100475894,840839214,698222194,732016003,595163923,182316010,96246754,480116454,439243922,211068250,951282842,161872114,424775900,745188317,826294759,681143700,267475806,668625508,410585597,920594363,169015451,22950599,445576268,712808251,396724485,1336896,722467613,442999341,248591775,565543693,303923886,905561871,242715632,72619209,403310264,578326428,797364611,112494505,362594746,579809570,827386042,594718084,739126741,56041597,161795004,611665943,639263541,869352643,591780645,273757028,812964770,570248614,551401708,111142958,716155970,257151810,307846758,227784854,791186017}

Returns: 645340684
1

95

{28334548,661301449,720419047,173900868,876439651,487583489,218363304,496137549,191049913,44615009,255088585,539078362,561692986,557975268,782621578,527519994,568520418,125237585,408080062,645277644,42194643,338488106,215034153,873186836,72319703,290189752,585013247,763967792,39768898,134104547,514492936,107125692,516630936,653365382,932662077,814442850,944923507,523192968,896826791,836651755,229444272,322021001,832979523,552261787,987402489,743890974,953228983,249663005,949050988,936493967,948699354,128181287,303778040,774871869,310113535,187907141,89123880,949908248,901940589,673342929,162996987,96425983,513968692,396221228,482645572,261308976,285229328,513363874,368233385,900740497,318845299,473698325,879199080,571554344,962517431,539775899,778756137,276197492,529899412,664208917,889263644,508747446,752838069,869182218,985230589,210746824,956303119,759016066,340178609,73613730,704583669,665410124,540189505,36516086,397344850,430952677,359334013,120030222,956423658,527238655,112085614,418600844,744552293,465694314,322056824,322939581,604189412,438375445,159290625,293319530,987592935,73010545,621796013,305665414,420104667,438273090,825896572,370190643,88298130,681915305,850544840,560259221,742175942,373431609,695706504,208896534,870950908,463518997,852669619,110013341,945726149,894981184,643209425,224520755,194604727,744233136,159356537,712584871,364872813,414870355,154862663,531080416,710682769,77318909,633043095,644566806,338018761,945863281,249370092,784844359,283567477,77650220,963288440,950052308,943204081,988086628,133639992,84908801,145964163,442469078,832479282,897428878,443445818,170718593,271675277,947385664,179251739,744308919,230707469,566956712,575650928,587928430,429066548,796455423,81866515,611252830,835499821,850899731,874516038,154942221,340012377,782003150,419742889,993485157,635586541,185278534,282384648,866688586,956784534,34160827,602055688}

{578211929,906934149,346090179,162939482,575429515,912305200,477003179,196527145,583921392,691609720,756957393,29186251,466731637,447217627,682199404,781897853,481808505,430902617,791043984,657840235,412725726,342544951,861406080,95469215,599470238,313452986,154330148,215554090,240323751,873236398,260210989,356232507,270683721,80726738,476624138,579480858,201767955,721283530,568169367,856035075,387287654,490100234,80151699,935232221,103601006,141181304,836899422,953190860,337756878,748232025,372334002,116733699,854671672,255022751,686545456,90805283,485082484,624483498,954181044,400425744,28095100,27917924,363075655,728396481,982447900,393745243,113903964,682029169,334109040,818589532,276549573,153461116,894613490,741730875,767089193,445841666,947633454,765488018,173000757,181390833,663875597,368975668,319734253,570717233,671581759,513000605,942686227,3712776,598150652,700572033,852867375,303155881,914565557,520239424,325237004,842164318,748393585,788266532,356946302,448710217,347341932,707066287,978271763,307068506,841333446,574987992,713739526,238191309,298718841,562261047,726297123,750542323,530908775,711082552,509972277,434225418,181358825,590313500,863004248,268633156,275579428,786990937,732438512,783952668,279646238,501858694,728732887,635790738,305379302,18814128,206366054,71807009,247772543,150533526,817792327,808351920,259576444,228894242,345074382,208576549,344215686,841175171,576160293,169079876,248276784,610078912,925284184,948173263,978571973,617583462,805809548,994848705,319552080,73862268,753711557,966538147,607712444,544680000,440415555,392234787,655222823,487305628,909528605,110531686,900164407,62442908,306324287,401736140,406775104,681178993,680802594,98731891,824632559,530058571,971877939,349971166,949302032,947021177,741553289,446849764,903056218,8102721,985734126,710207653,877177229,559981009,256571926,186662559,306612260,773001794,270205623}

Returns: 414214458
100

1

{457728339,130778666,213449848}

{231857042,217711594,202193038}

Returns: 853216884
1

1

{394674542,445091364,293008335}

{949124973,746375803,206286634}

Returns: 785091553
100

99

{403462477,958467593,781648194,173229850,332574811,209737430,931731223,706203878,905336016,734285571,131287372,467901993,487943105,826217568,165290338,221867658,885264173,909961219,191941575,559498739,662135731,829506037,156801178,947309039,764145100,0,758238119,178322188,792004491,249402375,0,91029444,60564605,154904420,528287346,82383492,255838476,149889941,398027372,426107140,868191504,899442085,6951944,596669270,317134461,482870819,64411735,194953596,189722603,985351350,548862912,924686488,681263946,259221994,957543640,283889199,664958431,994792378,323825831,980843093,98130879,215852395,55927950,227028176,588929248,990710621,522343023,499205721,124736834,644606003,461377119,591310960,115273051,837410440,284006510,484116904,221458634,276069437,855730258,900401949,887409513,745140017,889178239,521654499,338072977,287589261,276949891,851215930,514531530,875287856,820778138,175374150,5604727,906583394,936134912,943807569,920286091,353136739,820987456,716368399,61921388,725076483,748346288,667623778,915034349,479670705,125191965,211273150,846697239,920028450,267064840,727146839,152510597,231359818,199806069,436322453,596855080,102595499,316011553,518604565,117251934,538276053,381398237,641117413,411209331,122690343,217155951,333725162,187376425,41843749,664798242,570210848,169821761,317031455,938379492,829424750,7135874,262430323,814407076,180702693,469877648,310450633,957680934,975784203,710851709,299332452,356871209,145550659,728762930,755322448,65357503,7824406,245153211,551670878,926494394,250131481,665087531,782202596,513495811,344073137,437051725,924298114,515591441,328434276,912121617,613664434,897619628,548281123,288821576,336539422,563498254,562587133,500831025,523370854,811329317,333370579,529183545,72609287,910850286,446880705,865647904,633458764,963961036,773853692,580272703,505355795,260159770,774558887,627150350,519641824,304266626,703406213,45402408,909475548,518589598,727149695,641488514,0,688006630}

{240883859,861080934,773398813,145302159,430559366,661269239,808928659,900617414,748925434,463177873,106056282,110222916,66546461,103359748,260772475,2045197,186686257,147981204,741899747,353840099,118901734,223480545,765480268,312081875,478680726,293677609,324662752,738404114,807304975,433608589,530230171,297827529,251130543,945625335,124868348,982575478,112500556,273566808,437847065,645897889,587831457,107529623,557869596,552267708,486386139,59358940,229918414,879879616,90193525,858469408,769763218,209665205,283854261,344673899,0,9444941,760200298,34990587,768359618,897696562,46845861,887442957,427075918,310055930,888176484,726745412,269442284,541197607,912700133,3565134,365428907,370873545,112558415,118031502,93536445,646990368,715760853,546545934,459117199,340163861,694904502,88793074,805919442,747596879,411222981,976974994,75819664,704121683,208167186,184048591,620043356,938187900,31293072,815703128,218203621,407858611,362868230,778377957,680428228,17834131,669993558,607907852,806210585,340636035,377068263,824084563,545219613,576055842,166592917,240095451,887225055,40097981,326732380,171382945,685482605,169247998,934701474,314392190,485654406,619781065,328203359,536627217,964256959,956284243,593632499,385442866,804354999,970078343,561410155,333513113,593484673,744475100,771599865,516399172,8282007,102435832,336255175,950208303,537275530,692324438,954573369,962482731,79233072,56722779,426590417,681662401,126582176,484159562,102737345,671119519,709701532,467382170,912004333,88663622,821228644,792760762,69237607,918105825,155050824,766197924,502182228,570816442,951696086,992426371,307066053,975295455,287744575,280484396,228033828,998355493,855611292,125007309,11159826,759108011,325940032,743128531,10467543,161026774,592961090,217017872,747146315,530205408,914649256,300297280,186605374,321933692,371207394,407768792,824996985,557092954,754785127,147860563,877571876,270286771,179605848,976319688,670134253,252273469,943862543}

Returns: 65009666
100

99

{192159552,841972319,266671707,326332606,445735902,299949777,719789313,420036742,824069172,68321160,375117640,972941241,631724587,303347421,60265221,78064833,335677605,787390136,870691950,176705591,404049047,273323154,106153172,452964376,178710700,499505493,563610862,694921826,998230118,523580815,709271281,686937818,873503724,757272533,187873045,552961218,176653817,354341244,310859895,384100673,502586851,817233936,49763073,284319963,493350983,910590317,504232540,209963276,166688120,605511943,548661529,188256950,387424028,554738998,425030488,20102033,664879600,487720408,867174662,879991055,273548907,256583695,283508656,302940442,980734645,303118348,859760972,678008727,932264663,226641908,8123176,479303430,447909783,93939294,94718924,858298251,210944940,654435661,673693717,229473434,670287415,172729466,625680846,566884007,87143256,143463849,562016742,497899090,237749959,960562071,526128071,165607732,734819013,533303942,241062931,67482183,443061680,634402194,10015611,758053992,12268977,466374029,700220959,268627402,409806618,653835153,470376720,716963730,78211662,214951666,510551033,534815418,201559526,391460819,797212620,277269043,297131100,379561169,116794409,542113720,116329829,43451919,723830260,682917388,740068465,670411461,949089653,550086313,949280853,410816494,725488250,84274258,480779257,680407163,669322739,820053294,175613323,50145670,603946139,135780488,659152262,835054450,625814502,175825992,878257281,392605004,135460198,49535971,681391779,682117101,653703693,420252207,605560641,429308215,978116376,491127388,831666045,330018279,294468479,726742543,669548880,176462807,523879166,195650473,459849096,929070479,762957155,874516038,432630713,995530625,324650769,648242530,820235983,928759979,721657884,859010009,556642163,232575245,459989973,843158470,289904085,880541121,557786448,462011956,47830941,551783251,466891962,394338460,324824092,696916281,310634278,333301713,966327820,227046515,977713424,873171851,960019862,305956484,407147530}

{932478637,21212287,543194603,221965661,559224531,975610743,203742174,834057313,778421568,563569523,89942550,309784362,856735740,713645374,601332238,796543444,618962889,104898462,55775571,433660301,654160227,860376525,257380570,888618054,896983899,327401018,762746818,105340993,236629052,505202755,309367236,717390700,16046370,253708139,977957266,82076543,936524825,396962424,961213199,178423347,143167080,33415744,138102232,729860903,942327523,211956554,908609418,754565522,743914554,260950582,363901280,486655269,783034692,923200624,608347244,185047689,304477344,429441635,592740680,582807398,898592859,32572075,484309514,178467687,782924729,810956133,434958379,518454670,864396111,942114326,410375567,424803282,77343095,350192596,934496712,745862079,813798355,737671915,451084514,729901630,288567825,0,59230860,968174477,810171800,275152405,22184625,921438507,817290705,690197940,888101065,680502935,698864125,742499125,274621780,626879728,447055417,700953940,392269366,47993602,117695888,995435904,790679053,563242060,107341813,832913311,27402803,188921729,478775667,681445393,32176253,409590678,636235536,285418598,340432323,179171006,818022630,691744689,799416255,241894885,322659896,696490346,495797816,232168467,469085517,511376837,297763001,721135196,919384384,67153755,983337956,3526511,405542195,928427323,642936179,799104647,800459606,922499339,12458052,726392901,564561279,463747194,19752928,443521013,330724225,702681311,86895525,740154294,851194660,8488589,511722127,885856632,599909218,922354299,709000892,542089977,278552437,626331501,757047188,305315815,378976025,902866904,458305308,83686347,921299357,632962901,783171485,206845593,167531259,292038912,206982267,419420332,858012464,800783537,289119402,52134034,298133145,510673536,996030495,653420654,584304118,328040278,398500290,971930643,765429482,222155846,664903766,162399584,131956716,715271027,577629013,10281919,849758169,487821267,695914242,916435330,43408839,911512364,245131780}

Returns: 226435804
100

99

{752528449,292630146,960492894,441854144,895281066,743799664,745398087,908654091,276664521,699942907,487619926,711794572,522145118,657814892,975229925,141686686,144888450,709866516,230206088,897491046,583875488,779385754,988490223,764500083,255997746,167439629,392236853,577359539,32645844,0,984123966,767731474,863657163,933123831,533279027,83660055,207021244,804736063,22820056,305223210,540022434,482391937,395624708,636102521,943446302,828981224,65152003,31277347,491309276,213525181,795516779,876005594,605578740,340478315,946778045,384660737,357742749,866718251,59736969,456797046,371521123,364736478,576478804,876649272,163148648,381312862,314826692,164238223,918847169,830304106,232367525,789054330,206021481,15172525,368017797,583344034,170881529,452600672,873134101,966108877,563588610,317096043,164909166,119744359,868769041,592641664,322922996,75736447,953147697,651759832,436936480,141747849,779468124,687790856,298102400,374004920,702447438,181965564,137825722,479148979,378876663,981450192,124587847,906248188,321718439,529939550,157928140,364263315,738792642,38221976,575288485,908801717,176896468,340155424,311668764,754618416,431430171,201902908,275911724,273870842,777915050,512207406,984221919,360113454,639376620,393299575,275675541,659599093,779608067,652475210,82163635,676396220,135842916,640206900,744824806,647840967,617118881,185604300,856718443,487774633,652949003,531991191,440711930,816348614,745578761,384040919,77804917,515248073,67504047,468917744,167401929,650320695,489532166,840799131,767902421,229811185,827790577,968694420,110137784,600557016,407173437,549718580,919524302,37341411,738983433,522699815,113508898,749635595,224899153,231656281,471162880,967947878,826992099,354995446,616788126,568187395,970633668,582407438,343489212,693162810,658886415,615896484,900779296,177242907,279802473,870234285,946968180,732917977,697212558,980561380,14312013,605741593,653758737,991667110,53906655,140363132,841328899,719987214,426625201}

{344876415,735688090,648624942,805109698,382531090,219026636,405854245,666157966,627806442,136973237,729629620,804915935,464859596,677222094,443741030,684353906,341282498,517589996,832777357,465768156,744057706,734949936,134648040,978540202,702737829,708879091,898938746,535157000,853950324,446970214,241604197,516708365,794447791,879635863,931279407,950337486,802917228,409775362,578686737,532348074,339376554,303031803,470822288,222887738,190160603,912850586,895529453,348693541,96925088,75379292,105788578,796830347,897540763,32757911,474061678,294981230,638682463,512847900,83884592,343798303,289706363,260360964,984683320,628532190,832211261,206903856,213094108,435785388,240766299,58688059,227642610,95649856,728032205,641322940,575181926,445506662,731456494,906802061,658487118,927284710,97437353,505106772,952211799,576941766,837706646,571912172,637175207,677575333,677232025,64343902,989194709,987520560,957546720,309854290,272888537,773279463,774450424,627278641,145918334,133352351,895917980,574291172,896815788,623913145,535442314,319083042,672260844,481952898,44007446,575203577,216640772,519332174,893259480,665955433,523323887,653422468,408308449,663102192,797832025,795952778,454517362,143677143,949469227,755538164,672180245,921439664,697083838,568269491,210465884,32937006,571064687,622835801,540578611,940363817,39162987,570344936,696744230,197647620,82885138,646244455,508567888,719729527,647038208,656137035,261753875,997097428,82993380,604719956,324659543,483470776,261836307,202007910,315009016,944700693,905084794,269136850,128048691,551595157,74941277,226150879,143146742,750644455,580508662,690334740,785199550,870542081,660448337,253677014,447290361,433046945,295476477,133271684,970681917,674802054,812058532,643041830,377766162,128516240,906167044,456609869,984068048,656137035,86760165,598427305,849085718,899208344,146746757,89522224,363872494,833562464,334307723,11266345,133606350,568080190,240576470,11742590,354197850,592044399,433487527}

Returns: 957104452
99

99

{789077407,375498793,37235839,632000561,95271938,165361166,878567812,103742273,359096032,431318671,894989424,653055250,143867351,638841084,444808635,266906000,456871985,35386229,670296314,185461802,659814485,774866944,820284294,812692543,165209257,436453097,308319997,667563017,511362615,562044727,860446093,291547517,798787639,694060889,753819104,43723295,14284441,766621662,523234958,741987260,114772883,0,87386422,789465650,819421634,17560695,362565577,247366961,552796727,833009068,646871608,363129308,102850784,829507555,971628501,757884246,208014139,437135984,796638664,172815378,186108213,53157647,278665445,221392156,203863395,470892892,585463512,384128321,883196892,733377511,212494311,133243897,23236855,240246466,188780727,942467849,145579454,879305058,355829849,159111081,132296456,103336688,666129940,854519389,136662849,144619289,423753210,11348234,395308386,731239514,262069160,712489619,643750733,40932177,441924947,881336064,65001741,37482832,390464048,383288172,894448644,917961974,823910140,873993404,50308963,585144523,624163842,660190383,185235707,842352092,703098894,838212373,908252223,986474714,45177626,428634713,840844877,504761690,324603402,131621624,509315384,0,408071064,641676401,699710715,140828436,239222688,952079298,978667510,785260452,842897637,517021816,834431194,533954874,867336399,829375804,213918146,173135693,933831381,416556465,296571213,300629755,969965810,562276308,369907939,485592157,655212470,488992386,731300742,878147454,418549120,945769517,242108066,906222228,287129315,469392765,500539495,726598414,781733099,181974084,78951443,283906800,258557045,299163027,125333983,783821848,363232661,122974283,101717287,349769075,871756769,870048675,302672984,978321851,61925030,26680908,974439207,95983210,662570147,55592185,994397109,402564714,753652047,263654001,605526097,684290042,204831888,833239642,123955255,974538984,501107278,242404236,831905726,960015404,70752182,489862137,486759246,696820288,573773218}

{634060964,863009807,144293939,680964989,694702208,170121680,155537823,335983377,334826075,422986017,404242326,596488276,433961570,281820494,755742029,516547965,871209399,126811004,699658692,701107275,731102577,479016452,109320032,915560047,71474282,751824423,583179024,565232874,837181881,680323975,510251848,235248341,899763455,982646156,946208938,76474337,244282655,542545986,165185449,265785016,925878872,549999487,604873236,705935958,96377254,920824590,305947442,599687897,816075221,175694050,767995858,947293918,759127617,326316752,48967082,495563438,249643692,292196369,211735215,923188767,623348417,272285239,902835119,509256972,83386240,400599315,494570040,498409092,406084606,264944059,783696724,645598232,798019514,234275445,721433087,642284489,493892950,318264228,600304499,891877290,70420915,316488887,948914197,907541449,126443627,263252645,38498079,333357409,596347598,6705617,62510385,937214942,883263286,705705107,764953787,757842781,514694118,860958339,999114229,239816836,57680934,615169338,553902181,396055218,887194700,761434969,997178994,725110186,823406076,594645655,307497301,280379464,904370893,338418066,974831950,580384872,10409882,111672650,596646541,555562254,53587279,106840199,25150627,564462741,879826662,574973854,295074776,160666102,76815727,826453845,219159079,44158389,447347353,913799906,484604681,631844135,952776255,680394111,671177702,575843286,354365828,332938623,341235026,551038674,592200548,422955459,288152324,537660624,241039445,624947192,969402695,421811056,990087056,371390897,624362500,457501769,134645370,874516038,522950310,0,752078394,583344034,544167475,617502471,598278821,767209520,229389448,749236427,998409951,756500872,228060908,828698713,832840911,279713178,391918145,802549865,815420714,989032251,201119543,672929743,727652554,687494821,190332742,563413943,882826199,834755507,163318406,400266705,880200051,557664516,98280930,183669433,947309039,323312467,639336365,719564497,247817241,194951058,543013580}

Returns: 896618699
99

100

{361037619,341129856,328488880,6983902,511517143,43367272,282875549,497374780,47710071,122614018,219669082,811787806,215464344,320634652,252106555,290842501,574391467,438492552,136411520,579362226,879888667,50123230,255310007,600058844,330315079,850681727,919152211,454663864,724283742,142928610,626793738,719924820,555985782,80849815,718759905,478420118,325923099,943192506,526985022,555650753,914593245,639318808,294581885,304833473,929597308,593357796,504569274,196551810,445191351,716292858,563812040,628062574,504645175,652294925,274729635,517306773,71475972,888012791,927006511,472682069,634216797,547272653,926003026,481345876,757769044,974889249,775969531,917353095,896794959,786447586,386753226,970945246,515376542,559557697,124515165,943956048,226883272,584195504,920725266,329454145,446725270,783943986,52442992,460219073,820100473,998031512,126944682,501188945,596449709,773224948,990645427,37014687,925528575,759970058,321286174,184782450,178419694,536680019,392065314,119973156,745817975,718466885,228691128,338105676,57108758,538689439,313361071,277129796,827352333,437483035,360056242,93884357,391051135,96825226,947001229,47665263,243398629,173024260,867246579,305163110,583456600,582633542,807084574,29031458,803580806,921745562,710919446,888731297,598283886,603493990,316635460,128613827,588760624,295168543,551861779,987674653,979501998,860960861,432191058,585648033,786645476,37698649,545166719,743575190,521756096,51985337,864669906,286695533,970489994,717205373,641805134,890264138,994905397,746318007,199704262,254377296,30880297,790108556,954660107,864360850,637589808,340838790,946965178,43171856,603684446,736916131,806169872,35849152,221406404,897296499,337879846,581075044,178004120,968454769,293689434,353409002,973468755,670355934,170437358,913624742,673929504,615664834,675302920,171395020,314753968,703413372,18426446,931565785,405472274,690895856,4352575,803039485,346517,527454884,435183136,686482329,902567095,312548318,583642538,167522438,639522110}

{895127344,748817503,269249707,343724504,268638984,490163023,65064982,505037835,104045672,278246132,903516336,345725096,623467061,429696941,95777599,853156171,415699259,997235430,562665288,954848622,836774305,480943714,607981835,427854555,371058449,807350389,313949710,385154907,973395300,286604576,301018689,816389891,470458351,974923875,292679753,486200039,405307297,769420426,364339974,454500039,390518313,254789568,731311968,792206394,602644251,612412417,730736924,128535689,688662795,108325602,507551477,647151638,366863341,602134134,970330464,312281045,947716592,49856430,818936701,204365014,980469421,861194282,859111715,459856517,611071230,276856012,790902447,104600680,991000599,477055697,788384755,963299050,159040782,412458577,433138129,289669762,225198370,528516207,692810543,396269503,486353618,116521218,96665578,307018644,382963239,844131798,803031111,947309039,394169624,46237752,211024716,884500462,60859828,181457260,876661441,956211749,427095798,968411493,415804279,34653275,395402988,72197601,518977540,57635513,951151618,498299698,778353122,43095500,918988675,670534529,203922144,509487442,55380382,437826476,560675726,856237833,583344034,596917544,245762096,583840711,972845319,859787467,919291814,513508790,881880801,486428408,329370019,599129013,466468942,236730303,187617209,926863980,451379114,98017522,497891765,419799115,897950866,794899303,329163093,359888328,527325210,310821038,34213112,209668845,649380427,869164142,894388553,116132713,353023687,158821507,868262888,861192172,473659606,32835053,736174489,101664473,888889822,299591667,944087407,182180919,480875128,702321929,856543728,4229984,633504310,27946148,275875241,501943198,412437139,500633256,651173516,80984484,93334880,171702022,15494849,491320001,807248515,369279958,477971717,884538477,870917949,25954314,517475917,669993199,767260752,954997821,995875556,709280767,917950204,252426222,543912968,260648224,886151296,290443168,553866487,792576487,593044818,268388180,441471277,999298587,121846318}

Returns: 4381301
99

100

{778247042,933414277,20741216,232149763,717738138,442663414,140098711,173555169,742678311,41855057,562733685,429596120,616931543,509266756,451892855,619071819,898446616,532496084,594607779,402552012,663126276,360189031,445822793,476847473,146783482,657101361,608707937,75682016,110296256,330655517,371508624,631735398,809560636,372682657,672277844,222752737,397471016,284658565,486659622,995777496,876254985,0,600643503,633343706,714008738,676641950,202396609,233509357,419176379,300877292,251849797,215514276,182267389,640047534,429485235,89651014,871462388,834694308,548843242,261769033,770318738,621258672,328592999,711538784,335874074,803748968,606423196,805993804,96492395,790199586,539975952,857004386,253991369,999494923,738301193,11289358,690967422,449371199,428047998,295607642,484296613,461291716,897957764,302012352,705080578,801343233,788806457,540537594,875106662,156131436,75385404,833734234,353622537,651464148,519934881,364030447,69518536,465184228,738542845,297383445,811260343,343372491,168070297,915370581,174381231,809511248,147467448,940767552,640740049,695911542,501028341,433187912,193235800,389995527,219529060,98974950,581291055,166419378,641792133,466804710,9586845,177377428,578100668,847046778,79628959,164415535,517903233,291769174,698893844,403275948,855717978,599773140,756147973,768288450,541834452,667852603,491362656,622164433,755138443,400796862,119675436,501777186,18090185,203239454,532058616,920253811,821810579,914747225,365735478,825843113,875392995,529745388,126554380,781514869,93764417,194847090,241029623,833867591,267593709,975806149,127290098,268516622,385752650,596210716,975371520,151813207,75103813,8473545,874516038,964693066,724545380,865075019,367048446,91489309,957959458,928207637,702366675,724826639,238161005,985023249,126852912,630479820,225516379,823582936,51719956,560981092,414702807,156457508,82738798,708234255,987999586,715418783,467378451,820107318,818593693,727854816,322327082,488604735,973972728,261851908,553188991}

{40203793,454771114,331958757,687935564,984485482,951399532,432134512,912065778,323393299,575002383,309109816,400389214,365231428,82317722,362217686,14836289,928351754,770008910,42784,266016156,505412898,179890944,132723511,27806114,617586965,285192568,343205772,6544837,655557239,118089073,128896249,969139660,464459439,888382813,212987462,116743019,772825292,450587803,32743211,777937331,736191611,561602098,396503114,665916869,743675069,970445456,870987782,747872512,795813752,843218013,739992790,977732557,896410468,778102061,291456768,833001567,884753843,179035397,199191912,328536226,581950009,954856634,577979771,606951822,6619715,243406087,613006211,422137003,580378098,220663500,771694197,290949194,361435206,861129141,625085049,544154145,142732995,296552432,393578339,712392898,158748930,0,616218081,127389322,989528181,823566565,435811119,142415611,326418775,717271971,567203985,439090535,25107073,177377417,381570977,1718987,813383373,102817001,984995274,796869851,772070248,665422554,150595934,985437855,602481687,610216632,324958536,189394292,469023401,699805395,357569557,460367396,909228080,511861352,843885188,674446568,711419026,648132976,284336082,172823754,7099190,891371841,100174474,378367685,793937645,355191452,989169086,644254727,681538096,44788165,424751055,67727828,804700874,617420454,203179173,360621164,399569194,278129864,464534415,553685101,608318164,376165114,51255644,944385788,295908767,919055923,553531631,906451669,457906382,604902960,597548000,755464599,969131226,284236195,234947867,349447069,521725507,471592788,770127294,902667687,151485306,661761535,587119114,490418169,686133868,949665014,312135979,530495279,679075842,987421310,322184308,81830023,976633192,120344795,163988667,345464318,952066671,135556013,755528655,461390300,728103874,423551882,847713469,626178508,274025972,725940987,234821905,109047364,584134581,326646268,284289705,638655182,846776361,741106583,364302698,485930584,706533929,321494001,166030764,194545831,645546826}

Returns: 595398539
99

100

{741466206,818362578,196544742,347556613,77269598,857333944,660041685,150832873,20553628,269180314,191558787,173493660,628124043,560144426,121332373,798009642,463892902,964366661,171734777,19810483,526734735,866028207,606530181,652006321,61380017,115254291,620833533,41423591,856803995,437826381,465288104,817818927,335923405,101898580,303679037,462151199,344282784,512090415,519160810,515074707,785965914,583043875,675902005,426636001,671080242,791110154,469792598,865838394,940203426,331488924,759698937,890880705,728930036,212906280,817622522,897110807,702131507,534295921,264287000,871072167,94653223,985078474,337024603,544257631,772005833,649117754,99013812,685111927,986791265,883442742,585711252,261192088,849752582,529786950,694992650,405684002,820621680,91156728,49087104,912096028,797598977,156425555,118579187,329320319,269543449,36840416,886373125,560215218,514719236,5425249,284589801,199446591,729430108,221609674,15956247,638386858,598585437,217632807,375311291,872561872,113549750,118808659,676802828,85642317,532715409,680135086,288534896,265937382,162555636,222807972,379501450,612088096,96877178,834446879,283906236,62347569,833389976,335373813,754182283,601656330,905675899,711278174,11436895,963344277,298114362,814832630,517712639,867134362,42261765,270119675,234076034,479886250,491572363,544704108,440895826,87422774,372479308,609766260,371085099,596252366,958775506,843102989,66195705,482655919,260670409,613700284,657887311,508250392,676778941,793598230,61512456,180016503,765450666,222217052,860880276,196305753,58990368,352180488,672807685,969222516,187329047,495836466,891796530,553078985,570342861,6646004,94624230,33068965,450603812,935282044,165703946,391605956,287843065,639140186,207164075,639625340,616915412,76359908,417617076,232087238,968199972,393614251,762852538,202523321,110123671,239859638,950474744,285539856,146216199,120825524,488163275,483335380,0,718432230,218677585,244749737,677546235,34211900,415204022,753768012,272378034}

{881554183,291385277,279911619,846522402,740302807,385106250,461263190,436453697,659622220,154976172,627100872,324514557,667989924,94034344,425093607,672893626,163693990,796840580,793927602,955453738,720666803,897507171,302834736,936652057,682349435,151221453,263904079,925967322,469762892,336292684,345022937,581406210,565325318,669254996,719776492,952754303,438385911,754677279,537895129,50051908,300325253,231326023,83916589,553857781,999614279,753237655,897803381,659735765,535409886,625365667,816220648,450743712,390680762,837772255,585231195,295562353,522430284,458925686,257466242,662493043,653179658,124333600,741102118,887383220,792735360,957776364,330639184,974326400,625403203,958966418,980318994,393665586,324848934,590245412,17128355,433617848,132561612,654783891,637955391,710978403,870733983,828610559,511089143,170917368,284979609,157847927,31338495,674534429,635054634,315002698,78079724,382414255,827889383,531051249,186862812,151579425,475488819,557826178,635897313,311482783,855730592,285079616,816492846,110651923,117572645,340885081,1755132,838783424,887295214,43013015,652969860,552230777,48827255,475193157,277432926,403681829,317841285,243645993,179655222,479268539,322891616,25297984,40674309,579612611,536476083,846639152,747454422,259991011,546760672,918887685,6587042,39460752,351398873,142546662,116984902,196519365,706387555,750083638,352982795,172909843,833622687,307537416,330411226,684154013,828013035,372598484,330732154,397443504,73694688,427575560,878015183,79152668,484206408,440243303,64912284,610780495,900306091,222575257,443583021,752691396,442534691,705871326,967811706,164367728,156201406,667706590,321327095,873255066,329174356,981951172,725988685,972909122,0,642984997,414970336,324594349,335092378,831750181,540427160,379594501,821144524,504718155,880377397,547535751,336389326,478116184,208629951,541366112,823951495,68705834,73499328,208409195,420375197,995080354,25675540,373893960,113247425,173415815,1834499,94552581,403476870}

Returns: 929250051
99

100

{208377945,27816329,492887720,471907370,767912074,532721545,349370138,345513163,362924598,661927347,198998861,482091249,900607237,323626202,176721727,786576921,799968338,869356756,952831930,331269439,369723432,918080148,965029593,362163889,114287194,431431398,839784697,657838356,959082,851364736,304652398,481208062,428913367,448550802,521208597,782592016,215423452,180212111,509771019,439633747,970068998,831448101,191910422,20235604,415280108,838968385,750399245,788256212,625033458,0,845492640,255443384,458318878,998800738,906919334,708922400,452045841,520765496,498738340,580378143,174214603,812753125,481878916,45139590,669101366,390487686,3194612,83309616,91388721,798147552,161545472,532700086,320090053,547090921,17845439,8256048,414962848,81518894,533934686,942233806,603977720,692054480,427372623,583574193,433400921,216441894,700247697,530199425,90905871,574468713,228516495,786643134,202208444,198173444,491735490,262718849,102939567,276075584,190727809,838482497,936266600,86896305,747495332,721694571,855796550,139282000,867678360,206173792,344068465,416587528,680863318,123222632,392673766,530238288,160540733,462673770,954613489,574510028,815531221,264992185,381151324,962928742,397225718,928412050,675272595,68988931,870285022,963482639,461552945,773758916,934813903,203836454,281744423,765233682,939819985,808625425,387051409,705756898,154276660,938588201,331408063,638948469,290317404,574738114,323793493,189823128,452964964,264405500,206174759,684118646,122575325,710504222,700893421,616647775,990873519,986656050,632772920,495496917,51367175,640918724,680575452,724642206,388862375,193395204,194624977,837818095,502527284,675139908,164923723,454788195,241166987,671648634,621671467,528865147,24963168,841782058,7982485,821591393,344137303,309536060,523323754,185364005,448909584,456218119,71717849,525148567,586877190,393225961,395544463,585266759,635074688,82846240,662830100,143912773,849642300,40216587,315818499,309018963,772244479,128042849,915317197}

{172259417,455896739,591716152,842072306,651605494,189476654,408209522,245449494,721149209,812011735,788558284,791252048,55376592,0,355837653,92211311,716379818,318525556,598835500,544936497,514510035,166489372,763616025,650209088,787107035,918698281,205096349,914679904,736840783,775704284,748579307,441879272,371006731,668598220,38239755,668489825,706551302,146586087,9924673,190860763,621970527,126482335,959237780,790940539,782943621,832004434,550993133,67059170,813432317,170714472,165547272,878966663,962554283,766614763,780344560,461381779,686296052,400909144,671745501,522664493,613893520,772087331,360772848,733475624,5916215,749950257,582354184,143849055,200245976,589032388,892428869,583240822,731030654,50961554,766717767,599785858,170313129,471506835,132976350,236088172,989654451,391672015,87354337,510360245,424416837,217962183,649062067,907111791,856569228,184031294,101103634,686305649,222252073,944919152,572743,339007571,405359546,833980236,904725863,544998354,29083339,302133240,869691888,670625846,955935563,553536881,748302786,446411355,349598893,479900848,50311733,518144616,401996651,193490056,217017164,469388605,934325179,525694485,681526390,497730893,549728431,592778249,679378770,622265578,568548876,112865231,756595803,984870657,4810619,308825279,961297763,889214739,439733199,971890616,643238403,354812473,3039760,703181110,163089202,219501285,237992712,177932828,493516398,129792164,986079611,826039596,579005245,820611449,82298536,391399494,268443410,565688108,420375215,394994405,825501191,768235139,156647243,298405354,170641676,938431750,746828369,307020515,379382539,899649969,45667850,962217714,627161016,463421421,892298706,966284933,513386329,577257735,869246076,194019385,223426295,425880894,950660196,742721034,176196806,471669302,478068225,737708660,788606015,991858150,876897881,310179459,762711386,200083694,815212259,776391507,62938838,396682977,178360940,276250553,466068985,285776092,51330606,132838716,905490763,924530666,858387424}

Returns: 800319564
99

100

{263543375,764174096,439650856,804271831,814042951,904031131,696777413,829947259,583723057,225883835,506194746,206156063,292343254,351555122,532783373,763011120,677672847,738545278,375942162,986011625,258667953,250641133,570106563,735226723,576038668,223612094,334709091,249303761,348079395,503318783,826337281,408166267,833551938,520597246,108707725,954620777,263592271,117839308,899119979,152180549,647702583,989293338,574840684,687700842,978035558,782770786,265967140,915909344,622187299,815983706,520774339,395260977,597916323,280567901,897503755,642532777,591965023,136327131,494658647,256123575,669767039,185630019,57101221,727556848,244780483,271740274,453499724,662357966,189597690,589457643,626598795,875350901,225195753,660092605,133380378,507007555,973979161,284946055,696514787,351973325,593750785,360824867,622312420,143320572,926716102,741119868,233493724,820617386,87871091,168993586,795492376,179246806,335689160,900721130,369020090,144834172,193881050,151558447,892145379,201076206,660186431,804209772,322387195,622536401,606432191,8348226,138813863,832961198,50923247,501007096,944781669,703210355,871514950,887895756,725671117,407355035,431693772,326094873,582560838,212138677,61780314,132903702,262199442,754492584,830666903,402960164,406355383,953979134,213048792,570420278,525239368,40480562,386546813,499795141,575578178,293073638,256706990,43151510,936019771,223447799,966088999,195543831,399820603,964872556,619777326,575844032,188998048,996106015,126700732,856308683,328818596,586049360,670324346,808904082,843440544,445359432,26598983,858198555,372008375,433267646,464963591,480410441,539496631,837620974,363775507,254119235,1437022,341148405,616956020,89593475,349340436,947394583,232070038,746321219,783483413,213033573,720010379,47878006,493132165,136589082,199280338,658693418,220351224,290997018,19470988,662972062,873183046,72724050,919111824,963582161,986990094,298335725,765629452,399389758,73933934,813093529,287266126,140073246,919651488,671824800,696614144}

{969526165,677117765,913737835,544133863,684449873,50721253,209711004,792604270,438809852,545015859,19631522,623977327,186433263,723332889,870204968,391664506,360571282,572328231,644712740,660024722,90549481,273740767,53613143,504518381,913135843,608373297,806988776,851866870,697611998,656137035,105028562,652838281,243722248,977285878,125617426,171877464,170574639,770498130,659064419,414434482,682667430,602971573,578100668,466622842,147117412,689197459,433006600,660980814,598246040,957339085,882553999,408372911,928673540,610597414,478159992,363004785,354998499,833876992,373816620,168948658,146949055,146346440,10814580,555598863,142046921,504810131,285845713,479760410,607140390,515909312,410490413,683987993,931926683,296493635,175196196,189919024,388850260,120102751,60139620,480091536,217219509,829590450,315738108,28138663,372704464,323261828,373184125,364672675,680780376,905083283,828326988,133694702,640028851,390014823,928211301,889179467,595141264,687096249,629617167,808187729,825683313,586171296,411007582,349090967,838000757,849237925,25573089,117252238,498275301,65719643,923010145,552624300,576196006,31231801,708645329,161525382,603839440,62368950,40942630,606744831,837299373,484048713,475072734,867767794,280900098,184090698,820749682,349792920,291076867,105090878,714881847,301410990,509485102,396532100,700664573,324730042,502425299,112705953,659661940,865334561,773291596,519992287,394284664,942393910,632297414,766592326,617579072,876267425,255530650,631192306,816995909,909368315,60555593,842967929,507803129,63460506,275045765,795530026,947637450,619712019,750061381,168525869,938047953,514787695,121886638,485828172,929705095,240626219,387442279,26765940,118632863,116779135,223064073,167934457,131531240,974496180,413114160,302565309,373745676,318753489,802249666,810208679,859230317,193818346,223240239,583266675,646193644,443700245,679386746,805057713,800492741,245423637,324649559,710366941,724715533,752381692,920300649,105462154,211651371,861257856,250465360}

Returns: 465663114
99

100

{477189163,799175872,846877826,224182679,412540556,790192177,73327179,361638562,233845148,694741716,87235959,799307496,182855351,375544489,67347126,319421693,748777629,8487350,439365480,106773276,174359921,747058767,796898783,707259389,74768432,927979309,710733277,469838905,53527130,64891893,252929483,762199339,265824946,402051080,672726828,310427285,519335237,232940148,909651605,669565162,958403020,391843230,214054278,454541663,263306913,193230138,175706547,452251333,404902371,849123207,756008379,254427882,59256282,706977137,112847489,787806290,496967273,810114372,137024386,70117709,518267914,803609306,728384380,754921819,870623959,589325437,504882805,537112404,505412551,572223659,77134633,550668397,959777773,930667594,734585743,17411621,444032520,609559700,113524036,748784421,404084344,345743964,825778563,865947657,313889506,52687629,64667523,799992796,555984790,815408870,649636164,848835196,636832439,560762638,116543562,245284981,610559113,182330925,119077742,3496772,869598139,898241186,174821619,619681607,700019913,142117926,709274199,350384070,581269672,476130371,208732196,558783566,720035866,243364075,863221728,274392951,926299615,961399382,719131575,927752483,121545381,563974468,712557984,786497504,204594649,660014728,840364390,519103361,88521370,258123758,672735730,426650175,926706950,466269493,55776341,888535620,557518426,174850580,721087943,495077649,193928651,294063794,928970679,446270315,430138985,123779929,249091586,765570014,744715295,198825215,831707162,895321573,84107833,365320032,401629374,764663334,296392014,956527699,366826006,984648804,748592221,439802713,226868354,648835484,305557058,269352087,192123874,597608478,836840830,524311837,460039392,582922243,167249951,195659429,462690917,450055594,828664504,35766981,131789628,10413382,953194688,996629882,32629708,703875014,697561438,230582093,316835273,39936074,152615050,354449892,379232872,885279877,88162266,853032686,628816955,770679486,448714016,948836176,874543679,782330167,425299447}

{272373093,563219556,640755770,588754005,691495615,595754828,907932790,218536155,497357150,290500551,384363828,766097580,415906325,408577913,71082727,947902317,402267249,863752286,734627485,985807969,902193237,284961449,300666622,760278886,285437444,601298002,182589655,306099415,66375570,734296930,890912068,344814248,943917804,693221985,654941993,189090764,651444123,117387966,135921044,390200745,754173472,200102837,669541725,663388829,966948010,382127005,300011898,673087574,31144140,628312804,32445977,58106504,926876084,442971677,216536756,254383022,123907055,669736450,654335766,29931004,252988013,411385589,616630310,0,428187804,601982485,194663339,650822308,874087953,776773069,567060663,142627489,613444943,690565,105786451,62848759,354996139,496105089,627748657,385834598,194835483,290809253,490867905,253191591,674485145,16879612,373863501,931052849,61603057,836034542,68680660,947790160,776229946,583344034,474034733,836013628,123603850,226017639,985952523,983103418,452730104,791873836,627247074,182068582,17399584,66356755,28298326,25075218,926199683,746324629,326327977,686910790,379130998,388302114,575572274,331041081,985008675,660942610,193444300,681912809,100745724,206600646,526244213,595853499,177703309,526299604,770897178,657713296,168550707,821771988,373612126,578926886,678159020,606525036,562506523,871077561,31987577,50576883,262083615,458056821,751132048,376256251,83258526,386231579,265923419,924807900,513948719,595509269,354818607,133592117,686850461,915584340,655248296,830597207,996157879,458518060,813576427,881879262,882386240,626139689,564916145,351094006,759659838,119983340,517065004,786603935,17756169,524796605,392086202,7810207,351307852,481880032,306538788,34274860,354663774,900471596,862052872,686548785,550773951,604257222,850606571,381541395,673463222,438541289,830082217,367975766,336327554,734486440,181992748,513541968,433071508,386063862,539025943,785386483,39312492,470562433,67745298,478456639,88315603,145740511,773425607}

Returns: 719027888
100

99

{27576175,193434127,548458311,72874980,366041076,409383361,293542040,394842205,439317974,97033310,40492222,193108879,464976803,325793716,861057233,347816220,360421051,273300290,825737503,138770179,321447562,693922337,339559245,439861763,341268495,121179910,395834532,550735849,324620089,621165760,691243755,695610049,18687647,925189724,130970346,469074864,823466178,829626963,743633933,200133228,911028449,573329165,722171143,68871867,551833351,725906788,877475435,363864238,21449968,52365651,786005967,16056722,929283564,166636116,836120166,865342042,165840428,462572599,854115884,217437708,106459347,928723811,961909830,563308603,66022232,658549873,20102033,396478687,363714509,204337026,913114938,867771557,841751512,488873382,364051312,758762988,974997528,898462859,684910414,436164385,364432230,191478174,153983797,752490363,621592647,172692165,274627114,547655954,447642793,576436773,604551451,8623132,869130460,206561296,689431416,224995976,157836757,396803515,714084939,102357152,82146167,927018216,740529977,378793452,174353147,67210258,791268398,326009290,975802336,102070223,742355139,941755754,524697835,127242240,535337733,689935059,190609508,980231884,439384939,800190834,46164970,675446716,527360937,835095546,831682366,531470033,794179854,430224348,656137035,532890321,975343477,768089791,472707361,495894041,340873971,344903123,813080769,198996656,974447242,588936551,891614695,630270845,261433104,945850655,708138143,732207247,86917062,397896357,882606888,818882452,697588059,797317662,732279341,951345692,518125148,154617837,2613371,634948417,216746096,435286341,724905027,203158402,203191357,287603668,634121951,895197543,277944080,572303487,221317068,417057802,845130507,502558313,636421637,379534779,909175815,967828694,579470354,680136967,886348095,110651416,626926186,440603338,362199250,262630451,497988244,978770574,940191800,418107121,188618485,38778693,389171003,326850995,176694566,578315355,775762296,793343881,528462906,495534621,152637225}

{194895708,225181760,507471638,585393824,425216888,900434461,715172769,450147464,7422806,300643553,895604199,771772641,157978939,258008078,416069683,156819233,932811412,51377896,276458213,671198981,563970505,59723489,794671385,319230749,921018413,835052568,900610000,92892737,133956732,783142211,936600855,639488170,44932986,843839100,658966127,208231005,45432376,434614506,487581289,173757931,20102033,102886728,216002163,814910942,194780895,794936335,187698369,117669976,652742652,266257184,162630548,89453012,307309372,692212085,237610324,846548950,831633534,519676991,958322332,280125045,958562570,7918751,380573397,478094133,126537355,306934500,454098048,607722039,608568773,649675047,522974546,421476954,795810392,836825134,365889567,195100953,444009400,788069196,906843695,608887308,787381199,354713007,11077847,850962936,743924107,167992187,68878886,712035800,747646589,332278987,74286025,935537230,270978765,165327433,143020702,265177923,832000346,273708771,156502770,55835636,859509593,764260687,144287447,831628336,431236910,133141280,659338428,325871952,563261057,511468430,951365281,258129794,202924951,134138747,21561135,772034033,679562016,288517839,714536423,695048692,553911040,921281564,610168934,52295432,386409456,506127608,730536075,524768227,109117190,576820161,224272389,204867597,570437220,0,423659695,558015822,705123471,209821497,397518283,351514058,260615463,510551033,769274506,311349744,97521158,178182890,339426484,715347106,392943033,547027067,627121810,335729899,844717027,365140220,83240184,258869302,913494021,337505908,61206723,407657175,866857450,344368886,607285027,348128045,380144882,541812996,652752136,574984434,151037920,222897243,895112303,239298920,556409349,848353105,988946962,453822532,95565554,777322005,355330261,676339862,775197187,786166612,914283099,127852702,13538370,827789927,98517475,318075196,201332326,973559411,764749908,688359799,516016513,593021475,501594576,534838431,880747960,243076906,27859043}

Returns: 411460548
100

99

{158507015,890362687,108283040,250012519,436998879,559705756,240778045,952902066,517774008,172088877,252501624,535438518,404562133,969397728,390297339,762835478,107473833,125102214,675279466,138185478,540137625,313946612,651188186,560572195,221779339,60517877,773397808,274371503,70680520,465459204,541930603,968138425,264260808,682232008,92242374,983200038,811805800,0,653828859,201053411,67409693,751271449,296681257,673730343,442766831,447538827,873695531,585799611,628595421,715972651,338367999,279218244,436834750,997631152,156757682,805793887,494094892,810320692,210570544,508164855,31488191,798762764,573540262,39421295,580747541,960322909,935358811,855355672,940158023,447468409,879900453,798677400,81554797,363900446,95179035,628287676,796622853,764408103,231535862,979907579,585333432,706157889,528937371,896153278,74032452,837117390,992455559,848908970,186430587,136228501,789586721,896202829,648953107,821815488,690433107,8863422,906977470,409277319,792035948,491059250,485593163,346460238,573266401,651806428,752732112,772041923,6199814,770550387,707999644,103937174,664299686,432642521,662365156,366631652,878291288,917102259,421066589,334568902,366259976,359371806,285408628,600515733,643195095,332753669,413102871,112287302,695393918,972213274,648498984,943209005,8804103,430633229,727374198,26333649,594247160,168847056,611611501,718427110,667080874,989388558,514163401,220375823,943621271,829439084,151818958,529348409,29755566,459322371,289108313,688169520,641122594,402279111,609182497,371538043,929735864,278246169,94678452,864473525,184364208,55381361,711233704,711360200,345124567,16397834,280258110,272380124,600377388,546723104,360382987,7266797,619083366,252484325,50691225,186259390,720294913,366986038,183353286,722432591,655863394,492216677,640975,611414641,292514054,860989883,257720861,688312613,189499099,682881795,580462736,397579080,941076142,465193649,574702167,330290012,137098855,342264384,30024307,484723456,144474159}

{41985269,138494537,400622556,757701794,936879173,219012898,549049492,150787580,777875160,919887791,163064588,49972947,549478584,743268809,97712601,25653595,750092122,181024946,99537317,7918483,750784466,770910327,942451293,834156113,340154358,868580187,625265235,285206937,460546403,500491673,670122984,938752913,962890037,805478813,63098975,79188184,17012031,766220516,796416617,470419715,11301108,842724372,267290569,742257097,340963381,313467527,59803035,622620757,473207987,839811089,914406355,580564269,523348328,597733494,326201353,207291024,222118954,689887149,52233098,399816879,478087985,597870622,465303476,528872088,916934036,537868681,632120383,326311332,4197450,416247784,278624121,562567034,653948156,528344494,787384858,848742695,6872405,373566550,464619625,838227286,225963871,29427442,852785137,822181778,115993381,385435827,99021697,224949527,443826442,806571422,453128427,360053096,361958042,623625187,51702000,144706939,449767779,194705768,161193344,769510300,633883856,496644964,19447723,230803736,845951025,470733950,425303344,387958351,68272635,133689989,945050782,395272174,365664434,62229324,357003510,433776871,650523484,574857887,557454376,400182579,846650254,255809864,196012882,102603830,619072347,531334767,274064833,503552945,605488794,51470321,894720447,606058271,552021864,520322391,402494535,1856144,229661021,598312108,560691087,699676077,519900808,627916572,78664163,361097440,977244218,637950797,931326929,892425578,922996168,87096805,682708705,468900854,652328228,992223628,319501205,947066831,681512191,432923151,753722159,574081798,157811292,519967304,900569464,377982808,69453810,856788337,644325996,95955077,269648486,273700624,314108602,96428196,651122879,33279566,349254434,772608133,468313511,436373642,814768027,780160771,830040500,42552081,283927226,126785546,331272486,818556678,518792165,512500317,261129793,540436574,493793158,27171362,518261741,542994573,973269935,285528823,864822675,498623905,179525779}

Returns: 760176270
99

99

{799759710,726638510,610117395,275093717,121043565,1747437,915994280,425347295,831339565,630529846,977676928,545983575,402653938,892500213,759072239,400059922,670371110,888742251,10566194,158727984,967759384,583001173,376350358,748606805,906037795,361112787,220171241,746453039,208824817,457963455,328792725,333889371,475027202,466538171,491944531,187629917,405424445,773996480,455711281,172884648,671335133,520668285,64780940,141408607,161754635,763863348,803115655,460391984,732786704,348453322,240436686,919046471,902327786,876033037,584814032,895136715,250189223,769220380,474469566,48684662,429557981,509222572,397166710,871769492,679458696,342060238,954817628,769847237,528567020,938295822,840327883,914977357,331822322,980345359,462772482,436278047,39309855,115518701,874587986,367444800,555981590,720932882,668014703,59262332,859203533,962253071,442209681,16403969,960296910,990630852,575663765,320693233,591093673,949991645,871043882,129747804,425469847,644266826,771423471,165096664,195002478,566488969,869396640,740415730,236800040,313922636,502137355,41516443,6516865,873438713,959416857,561210778,534538268,108087784,349725688,583344034,711214097,236363915,544317598,891900352,382048605,865482178,761511784,688062219,236559372,368315264,501719250,250078181,173893237,197407369,910009377,211314344,232106324,673517171,887877330,270110629,584015899,579345148,135565524,869847584,264465118,984040401,464654381,385330686,388166959,289019776,250592081,357965592,646148296,723731993,506242844,247049290,555270716,493016751,949548987,958052528,425016201,363983204,518314058,382097526,132361900,81412857,930307887,444947392,451278354,441309564,652437715,575585409,657773594,837377703,188446152,569464465,805453165,811580046,169270478,115472962,155275445,666961482,740253250,769378133,380336486,816296298,554674998,73191631,413917607,402717884,252914134,231155865,112595222,144060203,174206928,305938308,735637140,646367724,840969366,77506412,989840189,306504172,813056304}

{565962818,995700613,376270744,962486264,12473962,14885888,951747563,436196962,519948744,769690661,843541335,330220396,515997317,916581259,870233732,430577173,125501960,522586760,308212695,404111573,849974387,995258325,570689452,501177060,233028743,872980077,726239152,56265452,645385501,228538464,680473145,576917679,765305620,961834887,330153697,25360236,323931339,689637067,518059719,205885655,855608175,428925838,826707401,761236026,329662842,38857177,641663180,810856202,639255724,537056311,469704181,7084307,117007524,146746644,400754130,480138033,964035550,955460229,470203907,139414902,740463887,320371,531194987,807344177,229324247,396386989,650152770,257569253,929385280,396531361,175137730,464862573,427658043,998836599,788950511,71001397,697599806,646049763,181554680,851203102,429673424,435596450,805321064,398731935,186415338,48823900,145999278,913632256,330144322,779889353,840985370,919444958,217035926,512120371,300627930,217841034,729094626,324153626,993704181,675791809,105692895,417964232,481051081,114019387,528622571,452201614,764230377,627456712,244711386,971795812,661627716,573857239,826939779,707142651,826117198,478503162,569939344,61601087,696364875,491833458,480648049,783999218,114511372,982443043,795205223,595882394,413719720,309122761,529077875,46840416,964748048,158547757,558060515,47850587,264011424,300832025,545600995,113956281,820936451,893083824,54724096,337584806,846916286,259201621,536856834,491200725,596110571,130449775,595894281,254603883,486400391,811873886,878232302,48061489,207771770,751941861,258248223,393203688,373044769,656241523,355360266,452770672,299909224,669958166,527057600,656820681,930926048,76506532,925466165,175825737,427508809,483168837,234203024,300573116,810361937,825983425,388298838,371800285,933858382,401969059,827176498,103029801,437133798,761407328,884662164,917898670,100065168,607046655,915938205,218540853,745843104,698748672,218172867,639190122,600638568,999286692,947350974,896682997,241878968}

Returns: 535097838
100

99

{443948258,242076053,268555701,0,393520039,867959588,783952240,734061741,213371258,636747284,778459990,982701019,677903048,89617119,630597010,721514965,279038601,893645661,971264385,552693526,623053681,859107655,684817762,579484500,862152275,971061742,204764501,370713704,65907667,278391697,641518007,848928864,580477759,917275118,615083977,23443841,492237645,215087690,345366599,867905784,324263111,63889297,53231467,241857519,150583523,353686831,446250173,82743936,356431366,842860710,141859579,999701179,389223195,106244191,286010873,707061058,653092850,415800490,96651132,463575574,713945325,465433776,706615121,793815047,671801318,359151620,587107523,478634650,413187975,829399568,710236645,772402668,534280755,977873681,636842391,827582904,88479420,997406727,241874931,825214525,777188899,210225994,255839581,605785298,976447543,433554910,867302821,796076327,670332144,58805472,65297912,761477546,486227181,55279631,399588223,853278465,368621062,642267354,37951504,655181168,20102033,415017430,529363228,302736479,888793414,435530745,127239974,233163731,638984724,944047702,711814447,791451110,953719169,704660479,701851,753500065,331372556,442316463,803477547,489259912,17064261,475638090,322772008,740149405,932476611,167646702,105692441,538855288,191882237,627142587,5125765,671540722,476008401,170300557,10864648,436485186,488219917,650608524,546122549,713384296,988155034,869398316,970057200,346352627,7397025,635149755,334167972,799390007,802371940,221052744,673536208,336717080,35641766,916523214,809388116,501381057,294483679,404679650,322693586,176991693,512971569,530590905,813200710,688730741,865219388,928739282,136509555,110670621,205103700,509403290,250238364,431121973,590147724,60640157,323535450,325017417,541792221,312760376,274085644,129432242,378774805,860857204,685008683,730953602,904084118,860657515,942534859,126337162,257589111,43872341,785003888,779954192,194008711,892829130,497090819,424155092,473985263,791892288,969561496}

{760970001,620143195,933550058,413904681,883537660,800104375,551770843,719800817,473819396,804183058,123134361,202862520,318594725,454348790,987880166,924404308,914915712,211921929,209462453,680833562,775808325,487371698,696427759,824981165,57927437,434986671,93516980,225846313,346514220,675663089,92991189,72842029,756192149,794621212,803200484,493833774,338400591,21455179,958807014,821613743,384416806,560420050,857266976,842254474,776147976,350580385,784987287,746684148,644855606,593361734,364259078,620920951,729411440,956367274,373409244,407865035,106397213,939632624,124249043,977976723,930719211,993632317,514729308,810699040,847368360,582355208,906447085,650654258,844105081,743896819,239597155,870224934,449398273,171352241,227779475,477060481,6985892,315290725,486268685,880359677,78188392,283439269,788837130,781518059,714725621,190530550,499001521,179399750,437018081,520804672,891289249,703823355,530873965,786032560,474384046,454244940,671443558,906452693,753125275,293104334,425119085,184315557,917188170,280585042,261281732,263669860,173893024,293993515,994966778,260140359,288038347,519587983,403980806,28617601,357350917,640532310,514325356,772951265,282396396,208320718,894426672,219041082,128050190,579130791,351241858,124506770,198327337,636226635,394781109,847682879,618814021,87928854,672576746,954761067,738448287,550765801,754082925,974591204,182173909,690474597,100887496,717161447,556804999,895861044,19385259,747492637,677876019,470017727,257074914,10059444,444811994,731786152,104990840,111851469,3135885,744770163,552841411,216910324,16009901,685744869,258941865,95786729,783549118,836029978,439029554,13873934,600090731,479753749,491030131,867844804,301104164,19060047,249731342,546004718,958878764,123534772,93035224,543801716,569531999,401731612,353397717,334521466,654102645,237632007,518340200,488943342,908123452,670865875,430544161,368431280,411188,678131404,313536147,959949581,854094506,747875409,845870129,30580137,774438095}

Returns: 61137591
100

100

{272085570,717920824,643944009,598702714,507650928,296444991,456903563,360911130,465035732,209592596,42083709,736280134,344033209,850029830,876590634,234013184,556035544,454403999,722897026,148236744,832240154,953814455,338736196,305254782,338854614,922625905,859060841,947309039,663228301,21181505,765624839,154629382,838475149,466083975,597471580,410604359,462505727,684955855,183889505,394710190,842908955,821050734,284877154,63015837,982547950,43721750,488062148,450092461,893268261,818416377,909602519,707263412,338006023,35609367,324534326,561507423,384601520,581110002,78330223,976073461,998032717,663816235,649107669,915028841,676275949,489050175,313380010,308047510,203779220,728930036,491186542,801723037,907528461,794655240,984312462,984056177,809208682,29601490,259658144,668319225,677958467,228735066,178138143,503220011,537327946,82924519,863845151,922338490,625140260,456782459,600039178,684422692,45105427,767931196,90317200,634750405,410879486,510539598,57215347,192928096,498189975,476379935,18500985,870445243,399963864,227843078,449796801,905220320,450601583,652948509,566564919,611134317,646164870,135290557,597906747,26608656,367535924,762145792,55421082,815508616,139296517,440138972,64487056,690221056,451752272,0,704866974,740238648,412160787,987784570,849115525,0,52326472,324933682,795995758,492158226,808526017,387210566,820702150,172964388,707721986,811815646,211475023,977590053,475209950,765417164,111549413,884475226,497625073,319742227,543381578,266157679,533207929,140578639,210038685,615226045,782851161,197897477,816436220,194959365,525279230,864276563,679145684,379473464,810466028,325626462,11376228,94454424,834375116,780688253,602246542,449411854,955097711,794081018,354081202,331089370,917562789,886732070,701115804,89241816,97129241,126697157,57525936,100481490,806287985,148642381,960637159,216455553,270474912,536162703,604933223,197489182,51457802,208817442,928900206,325011299,551744143,219646202,572064171,589203924,62463083}

{957008739,851062929,184000159,821253193,230781119,592686803,871584679,783066625,653043111,445289246,940152730,120738599,184746097,402364237,481559797,29906352,525513289,165704255,445103724,282196027,346958763,580904282,349035465,799116315,436610295,633189324,77497524,49895253,476655440,388997135,775791005,572115063,383467634,499091591,860059934,874516038,515019323,571122206,578418678,980211108,70672179,846926606,812253810,753152912,310764911,489510689,903746033,289812857,516135760,248975022,28695744,656562685,760856652,970387365,431417699,263018419,516738495,871754094,198961505,811589546,545179246,901844454,236557504,118200298,934300622,805846424,987337672,580400565,27292666,506647674,989518699,594396522,867432708,961823115,615901512,279649707,891897556,611284931,884710626,536667200,198387545,289502281,257006589,24467332,982251939,7832699,617297521,82916091,423668000,114390748,375770242,50346347,994518336,319325014,306758509,279522742,241172052,39456129,116844749,224007482,387613045,772885570,937815012,323512484,651336255,809768128,149418451,630889768,580808948,305418456,765342050,50638055,466527738,423003776,965193233,290999646,996360809,438515740,875009595,620537011,4287414,10521319,8494782,395158480,821665090,231609360,744598787,915405077,581162225,197494538,248213678,407024087,744673989,263964631,702234407,557039238,155364938,313484732,802841500,61307073,760162533,787629728,296877091,631911908,411281374,571721424,922567184,957569779,494521132,20485807,758625472,314994781,758017130,190372396,144125819,947309039,188941678,351205726,3685657,175050983,946435702,234531788,684268093,657023759,204585433,29033699,83438667,899374733,742522616,681964139,53493839,657537385,687952776,526738542,331880985,487692400,772927950,737144298,374890473,915716814,890496185,347878376,259806971,354024710,966346282,652339793,270052481,512280248,863523710,388346666,362712649,293844365,869071849,930705604,594605912,522370123,238645553,61959293,994103197,77477191,665647751}

Returns: 872400778
100

99

{841967238,82931446,248014906,689516388,980184818,849322185,871103471,11051649,728751344,28136201,617745761,851149824,519895913,305704935,980790771,708104757,759442517,678643392,94444237,628879348,462429255,866632689,247238234,318889514,494120670,30055981,175248254,571443171,651200243,999492144,317607035,169823005,967196613,817974843,255747705,443529684,489198480,302493010,547791842,266382462,570276424,654990463,291111828,176376987,142067995,605360707,305925539,496080605,549088451,369125931,25819714,454790402,201202838,396234298,663255038,314833404,116999592,265821191,508963534,239368018,395772695,684742309,29506347,396248932,758288718,283467948,965848611,754645265,166972577,183472875,791536577,889957426,540471381,164640658,517596107,514933038,491988,481747894,712428359,660148609,150491390,708112323,45354402,651910683,929904100,626532862,86819548,262272352,656801894,461928426,325546391,677956627,676088675,464291963,520681237,318534481,803636553,983284481,438082963,364941890,737718509,901825303,529085309,221115961,514197109,927619372,538517158,96600692,629139654,70340382,463715869,534308191,823192774,220854842,513600256,722983861,367477450,745284653,389695124,691803955,506390717,520249361,123961086,406044299,383326620,513464081,514424553,8612674,189009951,8314212,427738762,779839949,109498132,203925092,587863537,890582738,143870282,433776605,160484007,944413042,23481182,199778229,405153404,108112122,496129041,46489907,146605681,773763159,110701170,633576302,244459051,249250291,34140092,320303918,961854214,775615814,152976209,815160722,18306984,458335734,259303074,739448786,646794311,974427971,411705653,345050332,16840524,833256011,784089873,929874703,775827335,903400597,363110172,251184134,394764397,278427549,16697643,560685397,844333733,489476556,607257788,118282016,973006423,981087337,764110079,234828377,408267649,291482498,698628520,455387155,724103346,675931551,274641510,694989290,900089889,210415809,738444292,32589966,946009144}

{889028284,136699355,483181435,28750356,412399020,43501573,328139862,484379323,580480595,501487412,47996472,140406278,566683238,536772624,291803553,941213917,56471814,474945496,683663726,814983355,420719458,760328540,254060421,222164786,235628734,831913321,660298744,399259695,171594021,655021976,321642141,113282120,429092661,960590847,377885997,144840557,784535009,894566764,655269129,173255344,571802439,777129590,274252767,420406576,423720509,693431153,465747919,755119481,181703138,480855184,384045157,369640777,140644273,841781318,179823592,42033481,159736169,602973095,268686341,39328168,542370451,780506563,297885400,362191587,967589128,166725403,380884087,962211223,608267183,690779356,454135928,190972172,938318107,554366444,178795384,593947216,876847407,627910461,810486390,970047640,2948492,79000050,548264347,651638789,425737892,247952804,929058967,581585584,232614600,489694645,959555719,56835749,382033784,814492275,472829706,751871030,383918243,401156409,602681489,571321824,564933379,178726816,162999260,586838273,467466806,636311147,850578961,30814773,487702935,355918725,926970284,235415759,823330978,914338471,95898052,246197919,790794850,243492710,107518181,463725671,815363004,351729863,258192644,648452640,528664156,235720340,467753735,510683311,645785145,567318080,272516326,817565207,850137930,637462479,505367975,297588684,330664810,799774885,569199872,485646490,343523104,440197465,605990221,406279271,251912121,293774879,134772286,274173857,461226061,985050351,242763967,476162833,460659717,753590051,366122511,7109073,349629338,935791883,199202803,511115951,92092569,284561473,484288493,946938269,298652264,203695478,635723178,146596945,5951908,297107950,259123010,316697437,193988939,499319717,794033744,706654755,96876056,814632131,176509093,101451325,612476221,402753061,300546563,535848102,640824091,813214385,133143758,420489571,280305688,176717471,443896304,796802145,982981842,651075537,83334722,537439128,719936267,315738832,582397944}

Returns: 289442205
100

100

{931968949,299378547,659258192,14080057,626162103,369905742,402061215,601496198,834650058,206829026,896610282,47188197,13012559,601763858,222999921,197885601,82921045,990453020,663093863,411171300,33575925,764890762,940247754,657983375,505956903,204308247,700277256,971184518,579318770,895133450,939039023,361647809,504981450,152658314,639473279,243098669,170351251,842120900,260753466,469270307,208180858,656137035,449328746,869087338,523692774,617109887,687992296,28197855,825904622,241596763,518543216,366403159,756197080,859850395,422035409,657900461,836136128,132338616,892857228,29266710,716006450,339955213,302768053,79782403,692226891,323888172,165914280,341903965,237368300,119477880,995288350,959921022,564032498,541193869,821365080,866407099,284661984,541700482,682200393,272882257,196579732,544733762,410898434,640701725,825533562,341576554,484463117,580391656,146332092,943512158,195131519,770112199,357229433,541795362,300481937,117360750,54304183,754362589,788479264,649560383,724522265,704095399,215847765,827979003,195771509,681806421,994454131,188972736,216379956,300958579,872442771,884862628,882596048,185176732,292301683,399296650,370047105,625557056,105070795,936614321,738949155,140311023,483523438,591402781,974006700,977296000,904539356,947309039,648029345,416651647,165801422,927048279,262415561,130505541,12649720,954287520,533769249,568845589,733799251,578770868,643574182,524160228,727747551,762607652,864244689,54314732,465331051,573835245,195737821,931077930,248593832,422028009,2163155,528154600,437415622,409419062,792667482,14081508,400756491,195842672,404123638,333976283,750944569,705704962,335360429,941757208,764507523,690411690,380674444,20630788,847054808,706435276,711818487,766066795,612047451,46158743,339046670,434990355,373174619,129453305,728086681,574436784,451109973,235958341,297925761,553127009,967112763,89760081,233567596,836344527,395711333,472114629,37785390,189778356,883785968,336863316,479577703,166888037,146933209,537321485,942716406}

{998929037,554848182,660622500,334890816,788827475,439865835,258012379,818874573,283810132,427948391,155406723,67795507,490481010,926475311,624485347,515369246,334227731,889759375,208483236,44545152,924041596,72680202,769078880,368934463,803083133,980719524,750545674,787164675,473250218,471515307,704147076,777652701,488435653,692549188,515236360,582588448,200857835,196474978,209061911,892746437,330612559,811367904,956537273,218435401,79595031,460451568,257484547,455654865,897114556,790877321,412073883,290384520,663432803,85980807,245289453,444520319,588570081,688971156,292111909,384003040,941963314,929942783,712485016,728195379,40413513,413243617,663312724,105442116,871401094,894096242,495682663,877124131,497390015,41685966,728393814,801304117,547821037,337200936,881704855,190942799,836223959,213746390,667914191,448838686,689079036,467634321,507450977,851663343,870239890,556640835,373247279,706991337,553697511,729866083,454234190,265754590,404259347,503867190,598390406,706251181,548633333,174745831,434225533,654272090,109754564,37910230,303029682,591145952,974634255,106200727,749918528,197328762,954091696,145580723,683857749,968965254,798275212,280757228,300815243,432103672,494115411,278320037,868527792,816524659,248977030,874095799,510551033,748358005,22757247,822303123,840949470,729314753,401284408,31382383,259978288,927240127,821111752,3746496,852246243,783673643,118719868,555082361,215207224,177866600,970002481,749996061,291554717,193876537,240737327,617304984,539866389,320500328,714209415,708660197,981105630,493164532,292753599,720745598,796323744,337240758,2762240,234154007,377144952,440742979,29602202,819563826,713597743,742358554,648786815,695916664,49894768,266436704,834882103,499189979,889302885,662097543,245177591,284094856,243356449,816646689,382220439,610007897,61313819,363363334,987136236,690016271,539977884,354032910,803177459,114848268,660333578,45744012,325291249,176427736,874330701,416213011,525037646,484472702,763568692,113574422,645417261}

Returns: 147938907
100

99

{52,16,18,75,41,27,83,39,14,18,56,43,93,73,55,72,96,6,76,87,46,58,3,27,15,38,64,55,63,4,33,9,32,63,69,78,66,100,22,27,19,42,75,65,49,19,57,7,100,27,30,43,23,8,10,12,60,56,90,24,80,40,6,71,3,27,51,21,43,96,73,79,8,60,36,41,23,26,14,93,77,18,20,69,92,0,71,76,31,29,56,87,67,67,28,68,49,81,55,705942265,245650008,948042569,260615684,157402155,271565084,64898958,429564141,792467005,47340340,120150624,498721296,930325081,993597951,432913240,477868193,170486374,585798729,869463509,788343023,784915909,939937913,79531339,179331548,612059483,766314565,292235351,209543188,126530358,442626569,654684170,75657686,935562189,132034808,143830004,873638431,504972124,939889754,473236584,682714637,120873956,17376412,445927194,42130114,807691594,493006251,980771146,346500449,757442770,341902579,269354912,709509253,147651596,382781145,537061785,654719518,94555496,384775931,193901613,152757233,341375887,291669817,340686276,509689323,764033114,689100482,912376918,205304,319099522,899064512,797009680,746970611,245339423,779491623,63820973,785116631,498251843,22065515,433129563,947495049,230016812,931937194,170392405,997896944,882278654,382279110,161719022,898118278,5908938,278694967,469857932,513760913,90591677,1785587,733976851,0,619273240,824231272,690117161,547250431}

{29,85,26,42,89,35,11,3,96,86,64,14,69,2,26,21,57,4,75,63,28,71,38,89,66,57,30,94,0,77,60,33,94,35,32,91,41,50,47,71,60,98,35,46,63,62,47,81,94,70,75,18,60,96,5,85,76,9,100,24,12,19,58,61,48,55,10,74,14,93,62,98,64,8,87,36,48,42,7,70,52,45,26,9,2,20,10,25,43,89,62,68,11,91,55,79,16,18,69,436504380,20535037,142120759,283339670,74857932,792004851,142918190,557440364,397251516,668678438,472277988,824265473,243428467,447311314,713252529,62808574,928228691,933529433,43,980266079,97294146,320459765,558992655,475505835,557929944,332450358,800275079,919266585,876043539,403723681,575825039,419633482,720684139,147570441,198608498,21177439,821887827,203708821,890296190,243821198,215617974,152018054,773523287,712173823,536376162,412853193,771583277,662805094,92411131,791205756,216248584,336249712,888673769,359257963,667056537,54466040,980874363,397597478,634444158,668308128,876380764,46617660,240663161,606167180,268316234,622671913,228468869,383206416,976376205,307187425,405765173,246702215,757641252,39335290,702953996,64133152,453048328,173985920,635689983,800867288,748868394,500560548,287623874,741946685,301223031,258484393,709116809,562370665,745478269,633911590,929735864,49096541,730135086,437139528,831051594,325637062,354966465,73168252,787563833,780739826}

Returns: 901979692
99

100

{85,10,69,56,34,77,8,59,72,26,46,54,7,89,39,90,53,99,33,8,23,60,37,57,37,19,82,33,77,91,70,70,61,96,99,12,8,62,7,37,58,72,73,55,78,0,16,2,53,43,57,24,51,38,85,19,55,58,38,15,17,66,86,88,55,41,88,37,58,79,51,13,80,28,19,47,18,30,9,87,50,56,59,50,75,38,76,93,87,69,18,23,92,27,48,9,66,33,15,48,175979448,771223027,854788475,826052606,229737791,182792620,246292496,693218404,761613374,685501813,369322168,564221678,464315811,598777354,45069880,211223593,113142725,442996186,239442535,525066780,467009530,48351620,315638786,584431520,264512356,250288549,293249543,712018762,158523534,869401327,311684292,57920663,359164214,527993744,136082403,89267629,677680861,633263626,326804000,618486995,117505817,173611018,49500362,101365393,292483201,656779603,222335076,138706458,369057649,354770343,18343546,109803839,444307972,375207946,362632583,366341387,395411588,597076639,681590448,144238366,134852165,135236706,426398890,474472323,908043016,67097764,398119497,151098307,399198021,29637723,10990781,714193126,641172203,377116186,794847983,480648773,166377231,93637560,75730489,547870339,722170487,296750214,496429718,970984250,126456071,0,954478269,483305928,539140193,432184743,129414257,719630185,131673259,598438505,650765272,988916168,414334745,666218471,486689020,759975942,510168053}

{920396692,45833650,977551007,186030911,545652978,929261485,331220768,103387363,783637618,68098797,61515114,902249353,960296013,214036956,626965218,378436814,642100850,620380528,713955126,145361632,972573492,865592361,583400542,552412979,164295147,134657586,222761355,620707233,955358774,309830092,634974499,682535118,961069448,652946384,968845327,192880706,762243950,472894813,66450577,284025638,755463054,104594439,168575625,29425768,582985816,752643819,688976875,339293001,941439484,945337515,518761583,607153947,828874237,354017836,772462190,579148395,251365872,557049514,889415325,640084004,41503047,401552703,25681366,288855507,959740988,697973608,71812656,943405889,370271037,630007463,48484080,110545073,148641204,19390541,494256348,12360614,728514617,171507521,315354194,470807685,266483656,6389430,579786534,731049288,449234086,419018308,944262605,494413848,798988848,129862656,617985226,949484276,801556333,306333400,205035473,629141872,550529673,205471605,230524280,45062883,356074323,12,16,49,46,94,1,97,34,45,78,89,91,11,38,40,46,78,94,78,76,64,87,56,41,74,88,0,34,88,81,22,30,13,70,67,80,45,80,46,27,92,44,9,53,61,40,10,46,15,42,24,60,82,6,98,11,7,47,55,56,66,91,66,48,91,16,43,23,22,22,73,26,36,78,57,53,76,3,37,48,26,76,17,24,89,36,17,20,6,79,79,21,64,72,2,18,13,29,62,98}

Returns: 878989299
98

99

{621193856,477395138,778401939,648714172,157104501,294451426,952774137,102441518,465904512,900865513,473299679,480497484,892526902,69190101,484434747,903587830,931115867,818565801,0,892932645,368978781,260660077,638277818,235320768,960392141,725786229,357055381,150382596,835650880,644761159,595756765,811745799,347514679,277305774,348583461,97746964,317488810,27691723,614506297,984866538,2575654,719972774,607563678,527345529,293640689,161673924,799543967,596612075,963845006,732509208,329700510,148211260,765317241,876312001,685298281,664519915,98693022,876024843,594870172,151106120,822328867,685947124,26650895,272905988,743881368,465252859,339453345,548572701,919255172,336347773,325774414,501320899,893417140,163367370,502332223,983938283,49046357,541116265,178393747,367191638,807829687,885114902,189608574,18230399,120595758,998113076,156601375,493711138,182473054,645210089,65380576,109309783,130701564,603550343,796060114,133314086,344806015,525181035,649592617,449915849,58,60,34,79,85,48,21,36,33,98,49,59,88,84,41,50,45,47,86,43,30,55,19,56,89,27,68,3,87,37,36,75,8,42,76,48,62,12,21,4,63,27,70,23,92,52,42,100,1,83,37,37,74,58,41,73,37,41,33,70,47,79,31,93,78,43,97,81,83,69,58,82,12,26,7,13,6,80,76,5,8,73,94,53,73,69,49,33,84,72,16,11,100,67,56,87,64,26,69}

{87,72,16,11,1,82,60,57,6,99,99,14,74,61,40,81,87,62,62,77,3,28,89,17,17,67,67,61,81,91,60,40,62,40,77,82,43,35,16,24,92,84,61,61,72,86,39,66,32,54,35,72,22,16,7,83,81,92,55,90,7,33,60,17,76,62,55,75,20,68,10,48,75,31,91,11,6,1,41,33,59,39,86,12,19,44,52,97,71,2,12,91,87,61,22,14,66,10,37,766516104,791494779,764296456,135392072,510551033,51486179,0,632881557,753744344,547747399,201479852,258543179,842127434,299844772,458638078,245736830,907763914,645508467,657760932,245273807,962091294,947262587,303712058,715587687,897147983,586135204,462757313,638285545,325569402,405881661,26575703,864791375,351318431,417161321,929180566,545699611,250691063,878434011,451691725,283336423,47776549,465978530,258584085,348515156,768346047,516113715,186428446,795308350,312661679,764678612,496094454,80519144,425889232,901570377,614289186,292804326,631971059,241310490,444195975,531639796,659010058,565501227,583677126,257318257,803838549,762357882,542340592,98038303,408514256,41408015,814173475,261644305,626709244,298342112,471601386,895862742,364052736,518499316,853116141,617191571,607575600,687854455,889990976,342162303,929415081,291981423,12821982,568751785,302802490,640181310,510067062,634506706,166340441,156340182,899664507,427136773,768055172,79314999,813202343,734777467}

Returns: 465004341
99

99

{618464056,346487731,616001781,439536852,518342564,78691411,293494601,999382788,644627778,475099474,796812549,854261392,300082663,853470853,153356452,592111443,684570949,256735941,712609430,836215873,590404925,226033436,60344844,578226202,78629691,412072683,646484589,830955289,115735073,597046067,800589603,483274110,928898160,707922487,77384778,617139534,996615795,227687121,573983945,410073607,34143617,353842239,554158134,121000876,204415768,94833458,619119234,175747400,570378580,832078381,350859695,181837727,952050853,670659416,256052336,371220241,665402751,376398076,161107336,784531186,349904133,586193387,985836002,162907171,602048330,624124530,606757772,314637132,267301229,306141901,570965608,585671103,225915802,335358482,40130259,590112392,601232292,929110173,292566660,416622236,414914035,353486515,933563015,394899200,444815086,208554531,423748220,517036093,744612711,143691675,643040658,398713242,956183414,398858204,541990597,444570195,785798550,572868169,529738624,958092627,13,83,9,99,0,82,42,65,16,90,35,58,62,17,65,16,28,63,6,84,59,58,5,55,98,73,86,74,74,79,67,94,28,30,10,34,93,41,39,49,39,9,54,92,12,72,70,9,92,83,53,70,71,86,6,54,0,11,99,83,81,1,67,86,18,50,88,54,65,67,100,22,60,95,5,59,33,74,78,7,36,79,75,10,4,39,40,81,22,91,33,56,71,39,53,88,62,76,75}

{810652394,617023629,124025491,745580140,279417843,216319196,563937666,644451632,752418311,588895080,419437203,181817557,738984177,205121722,206385183,470247447,87148103,323176297,945076039,491161208,305377515,836596052,456999165,569577041,236107774,968137549,229162862,572377490,831795130,336075017,497578335,114783212,962964096,362176111,424535242,372800218,724283204,233370078,294094762,321526325,84834769,283002714,502534326,919274274,702099582,19204749,295291456,146631079,471116015,14511806,43197421,826743980,678448827,110940065,405315705,611040626,888060260,325021219,476159885,232525909,221556452,297215208,717353768,504172869,693877614,384794482,672772556,909199478,721362791,896229738,762886263,947188016,91486768,896238821,313723895,225975395,633698909,870401489,348880276,675249066,528191286,842355521,410174852,212668446,710048434,598315676,786145355,734838933,150761221,892084572,559720966,709436837,322085702,668013868,676136228,333183360,465247390,266807448,25507529,196732606,1,3,58,96,81,50,84,5,4,71,0,94,63,72,94,33,40,84,72,47,6,33,95,84,76,58,53,58,34,84,40,48,38,45,82,3,13,53,89,86,45,22,92,77,71,20,44,97,38,47,83,49,61,64,30,46,76,28,73,73,77,38,90,76,70,28,77,8,6,18,69,58,24,67,22,3,73,57,97,25,31,18,82,42,62,97,13,19,97,10,34,0,10,74,9,25,85,33,96}

Returns: 607933845
99

99

{43,20,65,38,72,35,72,4,2,22,60,62,4,23,22,12,25,100,96,67,37,7,56,17,20,89,81,52,49,76,57,100,79,5,32,44,56,96,77,25,99,87,96,97,2,17,76,8,3,8,34,43,37,66,97,89,90,8,70,87,83,100,81,85,78,72,33,55,74,36,78,82,37,23,40,87,91,56,24,52,30,62,89,53,88,61,11,52,87,85,0,64,55,51,21,1,10,67,27,547110483,913420303,52192866,628987260,627832946,492615723,280731081,126613201,423617208,596566186,867724054,211949784,928437919,462735702,567336858,326341031,648010761,675467173,143040415,194542142,768264802,137719286,429919521,485502168,45791852,34881948,559952845,486891115,123529498,198795708,150949930,70403000,273256324,286584789,61643475,489821752,0,179121953,732876645,780098030,133391630,904380515,568742940,33398072,530688983,484537060,642385102,285081545,600881070,873819946,18043837,72253819,236291136,525376650,122386107,684958959,32537472,687319676,229891099,806382840,780302981,78306767,147113800,318488923,736449900,936377970,901483975,320905951,961485969,183611087,361968298,412083871,912713203,695647245,630150627,229086396,522175501,629856732,925573756,249097733,695014353,378870297,228775833,591633214,134932673,528459228,420407839,332530257,639316121,945221472,753905173,385455579,779653945,45713296,968159887,670386767,284964283,495113109,341243169,393702687}

{66,42,38,7,92,41,21,79,47,22,35,48,34,29,30,27,23,38,33,93,61,4,10,62,82,40,95,67,59,17,19,93,66,15,0,22,93,7,94,48,17,98,88,10,94,14,52,100,33,100,22,63,16,72,0,56,94,30,34,67,89,65,33,58,78,94,87,51,84,6,95,78,15,41,87,77,68,2,64,26,34,98,99,24,12,26,1,28,9,77,92,28,90,24,59,62,29,85,11,102024007,346097633,684856382,91148306,761187163,523896367,666702200,973467155,747625773,823428004,493946445,390839695,96723506,897266236,442428724,740846131,360459374,179687984,728244255,129596890,7310928,152977074,308009134,561496327,925276120,998783327,263312474,895276320,970258736,808326149,977760873,466663240,206381172,714446765,462913267,658857987,723287738,102894155,608970048,175089370,380166618,76077887,241963176,977335588,90380207,901945831,73279327,870710439,396865627,132305361,685252633,285363924,702195712,747182430,157677057,598206325,789280282,739320787,721176897,664266865,195080178,866618314,478467173,22407371,490855095,451451399,918122812,919381145,981930096,93857043,94494698,350041085,764282020,835360984,804942778,942808097,709862773,62755320,13335152,95097522,481716426,229901495,74122789,995976763,47011135,436116755,84373338,252051646,223804265,47381715,32503611,219259023,962291554,810284899,786856033,234580616,790572493,368577927,100420159,2362442}

Returns: 892196231
100

98

{13,40,73,85,94,41,24,86,44,60,21,45,66,66,89,37,30,42,81,6,25,53,79,6,1,43,82,35,24,72,74,82,74,12,86,24,99,0,41,7,93,0,23,89,16,58,9,25,89,95,78,4,0,83,88,54,90,14,34,49,57,72,62,2,85,86,31,47,9,16,16,67,3,45,83,23,69,79,88,69,84,72,21,41,23,2,17,3,83,80,66,80,57,94,24,54,22,11,436155510,338105000,153521715,977626161,655622244,313340538,273216389,434956848,612378902,706758539,151677827,875919652,735366901,673226094,680786748,674989877,82595992,504627519,464124037,805549996,866763717,314309676,861297266,570054493,353277406,514585605,794344548,159298082,604057428,107170571,139706244,384422682,149532422,177797632,725408336,552337219,732117959,585842682,278952462,407466829,750294243,405134191,959246811,151156743,221147708,690477587,319693762,687812197,274206245,797414125,706972955,410733375,40340179,145705685,653514300,448553598,27790673,865734710,834141899,770428421,587261168,745514616,705472448,566154175,467413283,595107372,104559283,364549079,792999111,196857603,48603150,336600291,466130393,419359147,246502052,336768025,878348165,755930924,255130872,123568205,614804868,828016317,269444947,701580998,232940758,16427314,482073536,434469253,819027875,563495667,108028219,211148733,301568913,437078682,471783217,853006019,616019192,912129341,660330637}

{793602266,212266646,400627490,697144255,898660139,764780032,414600665,228600063,542008146,946330734,977920133,558566964,949207604,536773563,966878817,481814310,759566506,504856126,664616136,695788110,50735187,585891021,454790611,176420060,55755986,643311206,289153372,304942759,950500159,974515838,992645179,88640513,806653417,496140915,352660255,844854657,698411621,270855851,365447901,5208573,820553941,677422073,394450312,754118040,49244228,361262383,419967267,937909815,655208409,58507101,66963920,619398407,528885664,853282198,70861187,446108118,458647283,342473827,200160385,444964382,38937590,151568374,292515072,390143415,741268865,60241778,410898828,829172290,530329034,61872972,984493240,979847763,998761285,283432991,811294484,899500894,310207284,821695094,687540176,536868953,278775693,119416398,905058198,652163968,308950063,454936255,11010136,471996793,608420138,48443931,662241637,327578069,89909605,63729408,98841140,259679377,17409811,965899894,608828889,50,78,20,4,86,44,55,63,27,85,36,77,43,57,6,82,99,53,5,18,47,100,22,30,35,70,9,44,81,95,13,63,33,9,79,48,21,73,34,32,51,98,4,49,62,22,83,61,90,88,20,94,45,47,31,1,59,32,75,69,83,22,56,24,6,19,78,20,5,51,50,42,87,59,45,55,58,44,29,20,30,57,93,34,80,40,41,78,16,24,92,57,78,97,62,43,81,29}

Returns: 913150083
99

98

{364097917,770730576,427842348,202517494,283650836,532378803,957994819,448796268,808484620,102214131,645190829,783752773,519617664,335304536,227117996,100097639,505701658,261917619,47002413,614932889,594412182,657458288,747781378,883898718,974221022,485136400,71149779,190387016,1114142,391471037,877962128,307783024,954673983,200762529,603933462,460769199,50683184,62165921,125491982,352927675,201999137,478445317,201522190,136686895,792838739,522074476,105108322,495233057,233481510,878213650,459062373,555836823,662430347,488616378,804293386,182632915,999560124,448268882,644795959,277438086,600234422,166873757,259255084,803599752,646592673,813913082,606301189,167731331,453320063,471890645,297231558,724502476,877270267,722824866,372266987,612992379,230019565,376981154,982807633,469320033,969279682,449660046,240076353,592939044,58565637,811302419,481933387,830476196,842942553,811371663,941043481,289338604,910108009,594923880,774402757,905956423,972170726,480549441,708149055,54,62,100,7,80,94,100,35,50,5,100,99,69,69,91,57,80,11,88,15,46,93,46,28,38,35,56,73,59,94,46,85,27,9,45,6,82,8,58,78,27,40,43,8,97,35,65,72,53,26,81,68,35,62,90,77,17,53,93,76,70,90,50,34,43,17,32,76,97,78,21,3,44,2,25,95,46,98,16,91,39,57,26,70,2,4,50,86,76,99,13,77,72,63,14,65,14,3}

{24,11,98,55,76,59,58,4,8,82,25,98,63,47,3,19,89,6,51,57,71,40,44,28,21,62,29,88,89,17,11,38,53,78,94,23,21,38,87,61,29,100,65,79,9,58,81,26,34,49,4,89,79,5,85,34,57,97,6,60,76,46,61,34,29,66,58,19,91,81,55,52,41,33,77,99,76,71,96,27,70,34,37,21,8,81,70,96,9,20,31,78,1,83,59,31,2,60,555177833,636677670,954269778,667507051,693446671,225466380,996589488,297248476,985898161,733262891,902273027,964009255,809853413,229607005,30217924,466728003,74060023,70263015,281918969,259808673,78126956,542903951,470252528,991584709,192099499,694158506,880632963,347406996,946402247,619543739,809604724,379865165,874595441,188584313,950283120,19347521,609187329,61040561,231814306,859256592,345548332,885499533,210536453,78623842,730878614,288611398,444060798,975561872,788765016,705853684,193008494,428166904,86896637,159312558,387440660,104129282,746526247,539876829,630341758,946574471,687817979,60552676,490885683,944638067,261845202,961988861,558015857,273172974,254232189,539073680,347275259,598875646,473360435,407851584,773446275,493763462,648458698,639961357,602417366,529220754,320595131,101528433,513410246,97013002,185788983,829278509,129838182,161445331,430750556,664746059,672045836,420693124,473512779,514155816,960691536,917394527,74206669,793452459,62254061}

Returns: 605950990
99

98

{517508384,965262445,123345220,378408864,43798993,220188063,820981155,841365760,710159619,875376249,350669818,777064481,557356569,487851687,996752142,625577652,741760253,118161465,753757829,828831281,639357908,574372533,869846396,340687366,285844734,514297359,801011981,36172373,190454323,104112807,330911732,276395491,549695047,283999883,429707738,469432435,660452542,631429111,210126086,388688265,566592583,925363848,169366237,839802965,190008913,872405894,31422565,374057621,918713201,708511776,342593389,308613955,250392303,793031042,265266683,246200287,347809746,581570789,791724146,40019910,914453760,275762106,188476019,625569805,129690609,34113521,792860195,812075584,67003256,232327611,624980612,960586565,137385327,639476032,80061703,960168775,576458131,687223675,61154230,68016277,507154523,680502030,952323185,446300366,547172088,933210053,749525021,401542324,10135370,23963127,779463392,689128944,91372313,203910680,995076733,708095072,112534625,308872365,602458479,67,46,42,56,27,74,35,92,68,65,75,73,35,4,83,57,9,43,16,46,98,93,26,83,48,24,93,63,60,97,91,34,65,70,1,37,84,95,31,55,69,27,16,61,36,70,81,82,16,51,46,11,55,82,49,30,84,90,95,86,51,92,78,46,23,70,0,91,2,50,59,87,15,20,3,82,14,48,86,76,26,15,59,54,30,52,53,8,34,35,70,20,92,8,31,56,1,36}

{109506992,596474894,579649354,221247579,803924251,450747581,788879435,390526327,198779749,629904639,29407212,977213905,572426085,703173638,738804028,799222497,189689315,333683394,403886036,233092753,65781571,260319728,323261978,94126783,131517400,476985811,865052120,406599550,694653016,467483155,451117869,664620315,387605411,166507283,948826533,0,378748391,155894273,663238065,663799048,472733796,790013259,83004567,314601512,899472181,785940445,685238797,963481436,623649991,164829865,646104462,339264600,444859834,848123400,526063502,262406565,90468609,295043808,431678559,390983902,480465648,669275884,5355213,175209621,186964538,658417188,913763260,543825850,45568569,187493600,565808540,124525285,456294578,342285233,820292296,417902840,497984932,132552094,821749097,837238270,304576583,748101952,965362890,526317716,390623382,559254361,353812175,752532186,537522403,505242037,538908613,934222369,111511115,992823814,20250583,953179190,359872468,720920719,361176445,68,27,69,92,34,46,34,16,48,36,41,36,18,35,57,0,29,96,53,77,7,54,58,60,36,83,77,81,11,46,10,44,40,97,6,6,95,97,94,52,67,90,25,24,26,64,3,25,78,86,0,81,44,8,61,45,60,95,34,36,88,24,6,64,15,36,78,18,40,41,38,51,85,87,52,93,54,28,87,57,45,44,15,4,19,38,73,55,3,81,19,66,81,100,28,76,23,31}

Returns: 408612601
100

99

{12,67,65,24,42,3,66,10,83,47,29,30,42,85,67,40,26,79,24,26,68,94,22,1,69,17,63,9,81,96,96,80,26,60,55,27,95,77,45,45,18,86,27,41,53,82,74,84,66,39,78,8,13,89,89,6,15,70,44,17,92,79,30,95,65,32,27,68,72,98,50,68,63,37,54,43,76,17,7,15,85,12,40,68,32,40,70,70,47,72,54,51,48,63,86,74,60,42,61,701763895,284986771,931688982,485609151,116845404,343025540,451554617,663095530,239077172,153767006,728216865,705069365,595591190,740179167,582648212,53429586,63816596,602706316,733833883,378743953,807416671,750224353,159094712,689784690,621812637,668428167,844863467,838540335,406174379,195385582,287400581,125925578,370003520,502294386,227907465,378215759,313703181,472311169,626948837,449942906,192322691,220669318,295702150,695669645,300645179,225507168,169433647,931661812,248379287,83896931,210082567,574954539,312708028,13656320,479202776,900749545,944341935,456193220,698541599,311489396,216372363,987957920,5916245,744934160,778292446,161070869,761107382,414687525,681577750,558308571,568831185,507810243,586670652,359026937,911260667,222823581,225361049,704573147,743401587,863959081,613637152,407571782,363643465,11912803,461632105,656102321,529712896,348630687,273137498,356812188,70037731,397802615,935184228,45130912,40018298,390530420,564948787,42275042,358039460,78257984}

{68,78,32,2,78,99,73,33,73,96,91,55,85,3,79,74,13,79,43,97,44,45,11,9,2,29,33,67,60,64,29,19,65,19,38,95,50,69,82,13,53,39,100,21,72,5,46,41,60,11,23,61,36,51,34,38,32,22,35,12,15,87,6,18,7,9,53,91,25,96,94,2,100,82,17,27,9,23,95,71,43,63,25,22,59,75,5,48,13,100,79,19,79,34,68,54,24,57,3,937189522,41416932,994720045,593557974,513928833,788444752,838255067,312774135,953181541,346535157,604708032,484075821,104302685,633110675,81450996,723351398,344324582,878036645,850348992,533200178,196356979,113168730,789125665,827543245,330673570,772584080,52114007,59486686,184826681,336123352,406640981,945015589,156340140,336967252,627923609,582208057,366008200,321585344,599336051,104500914,914055119,30213864,785346795,308279836,718568400,868509093,875998079,311098134,237048257,582446653,159908389,40585327,235929262,386938921,785526205,377069973,80138743,421054418,718879186,559159406,467963166,192788879,279508162,268136976,958571919,166897837,630226068,980822945,831106706,293164720,125384095,297078427,574157314,346323084,478261941,693167139,52445810,934112626,52806641,868274927,190373771,649120803,673953331,739659348,385073780,876105948,952705001,40948033,806560054,469630950,697349309,462866539,797837894,608373923,874516038,961154222,992422820,726193582,89031801,585769182}

Returns: 228991029
98

99

{78,19,46,73,79,14,73,62,34,67,87,81,89,3,72,63,48,95,48,78,2,22,9,80,21,60,78,57,15,7,15,81,83,94,33,49,6,67,68,49,39,13,33,3,95,10,1,35,30,100,11,85,41,0,17,8,16,77,1,18,2,98,1,74,12,57,100,77,22,33,52,9,64,33,61,17,78,50,1,1,75,0,32,74,95,75,90,37,23,80,91,91,81,20,76,79,59,17,24,187661518,648850668,408850832,635038949,374923193,438934510,332088975,519452446,954946157,445618092,120705705,328274900,490696834,874516038,612465823,19302346,84379880,25821653,617526684,632219799,755432672,266027162,321813533,20102033,534150525,662379615,239951665,724732985,859482636,551019414,403069614,103164940,474356211,647216362,698731354,247013695,370172602,322716572,825102403,838156427,980071205,823840304,412599333,735865460,145619345,340602776,721889280,833999549,855471551,971379553,809196604,877871971,749686747,218568925,659838680,547586857,250398836,88768442,965249109,347130004,203035495,563481125,565932757,896139581,738795715,845959680,344027842,401110196,782740611,784082607,988691252,651751152,268263558,738839576,642552468,32977840,897711062,923463930,901083578,343671984,715632387,270182991,115672273,651878323,493734208,980375357,819471105,353648875,327463163,20736111,154457971,530661555,996785427,880548067,293951862,515455156,835988223,350140145,439122690,914505064}

{279813383,572080252,200175173,51563336,215456957,511201451,398207371,481115041,34137206,699426273,281422897,508804684,982735635,733025214,935990808,65806982,894023445,665283836,646679427,530758611,658355743,627884651,894111592,645812864,515773303,911674059,835240726,595706843,300572166,888481937,127444672,972390730,948749196,376218360,902861389,428461220,266393040,450818107,740678032,857313158,214149640,443068041,546817546,125815280,91777238,76282859,636960399,90609404,959416334,948368239,492614680,902538479,441974145,393729881,97712336,637018805,89099398,331129126,126782009,583368582,273519085,576131628,246378837,522442190,310211446,890440937,948518093,910052228,894769628,467452737,100320267,763204896,238840214,735373138,934747127,968237749,500788367,90638492,354082190,495232379,46761655,448477131,395944578,945641365,424036246,63245041,273767586,104009417,465431715,369895097,175585252,276594335,588728878,413533007,34501633,150337341,91965765,752888737,559682490,620924298,49,32,72,45,62,80,92,76,17,58,22,38,86,49,24,43,38,63,86,4,59,26,62,23,86,83,4,75,18,96,60,97,18,72,68,86,26,95,78,73,30,11,55,35,79,1,15,53,87,23,11,69,83,0,30,98,29,14,57,71,32,61,1,33,18,26,14,61,45,19,98,98,71,28,87,13,93,90,84,80,58,8,25,47,91,0,15,75,41,15,14,18,56,36,24,71,48,27,14}

Returns: 178306418
100

1

{1,0,0}

{1,0,0}

Returns: 1
99

1

{1,0,0}

{0,1,0}

Returns: 0
99

1

{1,0,0}

{0,0,1}

Returns: 0
100

1

{0,1,0}

{1,0,0}

Returns: 0
99

1

{0,1,0}

{0,1,0}

Returns: 1
99

1

{0,1,0}

{0,0,1}

Returns: 0
100

1

{0,0,1}

{1,0,0}

Returns: 0
99

1

{0,0,1}

{0,1,0}

Returns: 0
99

1

{0,0,1}

{0,0,1}

Returns: 0
1

3

{1,1,1,1,1,1,1}

{1,1,1,1,1,1,1}

Returns: 571428576

The game consists of just one round in which Teja gains some strawberries. If Teja gains between 0 and 3 strawberries, the game will be competitive, if he gains more, it won't be. The probability that Teja gains between 0 and 3 strawberries is 4/7. Thus, we have X = 4 and Y = 7. We can compute that Z = 142,857,144 and therefore the answer you should return is (X*Z) modulo (10^9 + 7) = 571,428,576.
6

3

{4,7,0,0,0,0,0}

{4,2,0,0,0,0,0}

Returns: 1

This game has six rounds. In each round, the active player gains at most one strawberry. (Note that the probability of gaining more strawberries is zero.) Thus, the difference between the numbers of Teja's and Raja's strawberries never exceeds 3 and the game is guaranteed to be competitive.
7

3

{4,7,0,0,0,0,0}

{4,2,0,0,0,0,0}

Returns: 969874055

If Teja always gains a strawberry and Raja never does, the game will not be competitive. Thus, the probability that this game won't be competitive is (7/11)^4 * (4/6)^3.
50

5

{100,101,102,103,104,105,106,107,108,109,110}

{200,101,202,203,204,205,206,207,208,209,210}

Returns: 440607283
7

3

{4, 7, 0, 0, 0, 0, 0 }

{4, 2, 0, 0, 0, 0, 0 }

Returns: 969874055
50

5

{100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110 }

{200, 101, 202, 203, 204, 205, 206, 207, 208, 209, 210 }

Returns: 440607283

Statistics

Problem Statement for "Strawberry"

Problem Statement

Definition

Notes

Constraints

Examples