Statistics

Problem Statement for "ChainCity"

Problem Statement

Chain City consists of n buildings on a straight line. You are given the int[] dist with n-1 elements. The elements of dist are the distances between adjacent buildings, in order.

Citizens can travel along the straight line in both directions. Their speed is one unit of distance per second. You would now like to help them get around the city faster by building k teleporters. Once you do so, it will be possible to travel between any two teleporters in zero time.

For the purpose of this problem, both buildings and teleporters are considered points. Teleporters can be built anywhere on the line, possibly at non-integer coordinates. A teleporter may share its location with a building.

For any pair of buildings X and Y, let d(X,Y) be the shortest time a person will need to get from X to Y (or vice versa). The diameter of Chain City can be defined as the maximum of all values d(X,Y). Your task is to minimize the diameter of Chain City. Find an optimal way to place the teleporters and compute and return the corresponding value of the diameter. (It can be shown that the optimal diameter will always be an integer.)

Definition

Class:
ChainCity
Method:
findMin
Parameters:
int[], int
Returns:
int
Method signature:
int findMin(int[] dist, int k)
(be sure your method is public)

Constraints

  • dist will contain between 2 and 2,000 elements, inclusive.
  • Each element of dist will be between 1 and 10^6, inclusive.
  • k will be between 2 and |dist|+1, inclusive.

Examples

  1. {3,5,4}

    2

    Returns: 4

    The city is shown in the following picture: The blue points labeled A, B, C, D are the buildings. The two red points show one optimal placement of the two teleporters. For this placement of teleporters we have d(A,B) = 3, d(A,C) = 4, d(A,D) = 4, d(B,C) = 3, d(B,D) = 3, and d(C,D) = 4. The maximum of these values, and thus the diameter of Chain City, is 4. It can be shown that this solution is optimal.

  2. {3,5,4}

    3

    Returns: 3

    The buildings are in the same locations but now we may build three teleporters. One optimal solution is to build them at the same locations as the buildings B, C, and D.

  3. {3,5,4}

    4

    Returns: 0

    The only optimal solution for this test case is to build the four teleporters at the locations of the four buildings.

  4. {1,1, 100, 1,1,1, 100, 1, 100, 1,1,1}

    4

    Returns: 3

    As dist has 12 elements, there are 13 buildings. Let's call them A through M, in order. As we can see, the buildings form four "clusters": A+B+C, D+E+F+G, H+I, and J+K+L+M are four groups of buildings that are close to each other. One optimal placement of teleporters is to place the first one at building B, the second one halfway between E and F, the third one at building H, and the fourth one halfway between K and L.

  5. {3,1,4,1,5,9,2,6,5,3,5}

    4

    Returns: 8

  6. { 1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000 }

    6

    Returns: 5000000

  7. 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    853

    Returns: 667619

  8. 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    16

    Returns: 23316572

  9. {907825,484542,751095,106611,248176,741566,765346,38201,824346,32801,296270,449197,553224,156376,947864,654187,175740,957757,626206,215358,397819,921535,100141,103791,195176,372187,461098,59653,154153,757831,770778,608213,592914,558390,760624,84134,735592,333217,178440,318243,396584,303096,265232,348998,472993,647686,889269,635117,40298,391863,64572,766348,999629,353010,937480,596130,34640,126244,837633,52859,101743,495647,658666,625800,799559,976995,659098,667122,741784,421078,755339,203343,492188,736614,516453,907452,711332,827867,364237,247249,911637,784490,932384,595933,620756,209719,144943,267750,812781,327945,336985,24495,182637,173824,659323,587945,211071,732446,84326,88788,995984,373759,561342,184375,510409,304270,257887,785647,288271,45238,366762,947819,536114,138906,659408,499926,322336,382984,822277,415108,805002,898471,625689,756478,425160,247013,143596,272723,614630,631427,567846,363062,845573,936598,642022,182957,783714,997873,377587,119972,897900,20210,509049,733446,125768,513696,95018,522146,98596,459709,778508,560815,987990,676868,482510,129559,252890,517056,735800,949253,437421,89162,399177,531667,698471,181857,293734,454773,926417,936570,120472,81684,163254,107979,104524,355958,519461,441709,997445,826485,944242,297563,427449,981956,13348,151496,100205,307898,364538,20677,21726,218526,532764,173359,740083,161186,715515,708916,584124,742892,433316,723290,15075,686485,141193,811219,500845,788210,594006,599000,773048,818982,171838,850185,933204,488412,431225,441467,637277,173625,863835,167175,506648,104216,216249,898156,988827,90131,752844,94470,122635,681085,528322,51194,50310,854082,77288,542780,662904,939903,925302,723777,465558,519893,979191,242375,605681,451177,163952,528099,19737,11422,639410,126125,823332,393509,551867,768069,394428,426017,554278,592723,81014,447151,263094,560115,102223,717768,410700,638384,5840,623410,699465,785347,995348,185758,266735,95290,546095,80685,229675,736354,992857,443083,994680,465068,190040,227916,888143,571931,920922,792429,193707,85583,463824,666235,865672,943008,610753,183985,29067,619317,478044,769588,873962,403059,648682,181475,704909,101638,542481,955121,715986,466287,422933,612090,527723,37211,118543,944098,644269,426844,361618,826093,767468,282858,628946,564147,339107,302389,506490,741896,773383,705128,894167,893606,588745,515253,816977,102368,51544,850875,215197,798749,3554,174492,849037,618182,261170,119118,372126,164683,346238,72121,703356,923950,336732,172452,58092,370683,310097,756789,387431,522958,192884,576321,518130,810758,827380,298200,986061,146259,719247,904402,412434,510230,239763,605545,284780,201925,22082,798407,173595,139092,912977,413231,740764,240220,119885,720559,377311,972946,127619,297192,945738,610489,549928,387052,896128,602291,328186,335054,975427,735535,592778,120756,855725,440939,62341,273450,270068,679283,71835,611447,663289,334350,192475,315746,940518,933478,934911,821858,627495,818668,211561,893482,644499,599240,74879,27827,939641}

    14

    Returns: 14735331

  10. 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    59

    Returns: 13738727

  11. 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    1514

    Returns: 105620

  12. {193738,701662,235454,387082,12396,192370,456364,739749,231539,486538,508841,739662,155666,883481,400042,650657,654629,601418,696974,724657,998162,755278,825887,14758,176322,252731,421725,601486,309975,685484,84238,565627,674441,282177,269418,608408,934596,384683,73255,693470,421164,711402,349364,464911,665648,879137,942869,481853,955272,269397,819989,502344,369524,345472,526095,148048,616312,953411,714585,286057,998466,973005,454727,375292,10229,924153,648710,842345,388624,779513,166452,275235,925977,286057,241278,853465,987612,556202,260421,968850,472659,553408,331356,434020,906107,367674,908287,24101,456710,853097,322714,351973,938003,282673,277769,238637,268669,164793,238153,807597,443678,261371,175752,505808,799060,149308,315639,133617,240880,375011,367961,752258,152921,365939,228276,29842,897778,783647,282248,185418,182510,929572,260157,195567,72701,147801,52509,339129,107712,908323,20110,473012,795107,399785,110271,655725,743695,12498,525388,865099,832298,50497,780981,592825,105329,375660,737309,40834,536430,457451,592026,493123,407905,478572,880911,191584,816328,729834,249511,705467,733695}

    15

    Returns: 4785902

  13. 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    365

    Returns: 1025498

  14. 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    7

    Returns: 101073779

  15. {469238,727289,473517,424469,192660,176288,937405,69805,178014,762810,789501,512062,598116,509293,359889,656583,341159,65047,799223,357592,977319,153965,158795,224262,875345,728007,366750,675731,755662,427691,369894,301855,33905,526008,606045,114811,282416,263630,273632,461235,17143,370976,573250,205404,803498,616644,210141,291021,367118,421902,967096,942519,994103,937409,83987,576329,10196,490986,513205,958417,539494,984237,859474,266427,60656,641011,958078,493116,502238,492124,597258,62328,748617,118468,848541,619575,464153,468587,833070,706345,85578,16968,522431,430627,681257,135785,349319,305641,130848,315468,986314,144661,740002,788484,640360,271812,972153,185848,606000,337107,453066,87379,622208,708522,783688,714368,785650,754735,982996,557314,387476,329237,574911,431532,61245,419824,431970,309929,56332,237073,493352,294898,284213,981203,385968,260261,24228,148801,794715,19358,820975,519223,151632,356839,157217,895033,843565,899423,944212,261673,674097,594793,735613,278629,757870,518048,841618,917674,374066,831520,196783,623342,560686,986515,917932,586595,392422,674427,977860,594750,952263,609923,316019,449000,980653,960294,9147,125489,65859,122803,832798,696679,25371,595776,659000,526834,820532,889394,655771,408782,945202,778585,180967,118644,734202,713110,595971,331090,448339,868878,963970,959714,310266}

    131

    Returns: 406206

  16. {430385,136306,510564,361025,468861,718479,26435,211278,210806,324249,310684,881241,658134,952131,172173,718067,81007,616036,2286,335073,114785,658869,966520,154334,202556,32022,282581,469684,919040,440072,279468,842030,943114,51770,616605,18811,833888,686402,382895,855512,309224,998880,792653,909562,425771,207406,848678,475571,916033,334321,652319,835732,950711,763771,6180,410360,763457,159049,577199,310917,900414,428010,166166,521506,338349,476702,564273,564701,352872,949355,68166,43703,812183,17146,972000,895216,522008,548648,258315,536046,353782,671648,269169,341326,150883,819002,354710,53396,826637,840475,368518,787747,643004,658018,407306,276071,390338,243675,377168,866363,76256,407342,809393,586110,775647,995848,845895,267032,494005,625333,467674,328435,252752,995666,849270,321153,117882,168636,187980,745152,562222,930937,478714,971285,376795,508432,483655,321300,328207,449990,580470,490090,896697,457151,263642,530315,723405,300161,820555,561890,845637,731424,107298,217497,405331,484158,408702,590115,278629,27067,82972,109757,993417,735101,63326,343917,376866,531861,317376,189927,606479,860997,49562,307249,725821,51922,772779,923916,230076,759449,372377,343667,26750,177443,939064,578990,933298,153369,456814,540155,886144,163578,397662,121455,204507,348485,897391,343247,577646,452258,464409,432039,925571,563413,108672,350726,920982,10723,368361,827231,754119,633088,959067,372181,672422,912543,673572,124877,933340,136322,719868,621711,71306,836910,900902,742306,798874,248279,911571,156044,437174,411992,556857,565272,502312,868648,879501,921369,962022,578116,26509,575983,720837,826289,180779,22138,92217,396577,37520,478516,372550,211141,114663,75154,144608,979839,652305,809875,606999,134166,978292,762187,51357,468918,995361,275004,590441,466119,879855,944434,378025,233728,172797,294003,855389,355911,191241,952076,9446,722169,91093,999855,233944,579368,972172,912237,147915,633738,132129,174930,644469,19141,947870,228610,518224,343446,891494,864554,251124,826574,872282,576033,924078,751822,437133,655920,765797,66289,358895,23312}

    230

    Returns: 269169

  17. 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    419

    Returns: 2027343

  18. 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    409

    Returns: 1362900

  19. {639413,850835,78784,92160,112365,184724,595982,426570,398656,702300,166755,168792,883582,464463,157476,635763,867795,554396,106569,482684,864913,168473,421556,279413,142995,561674,351162,100637,958247,819592,816118,553543,738936,933984,195007,999737,943303,69964,830446,467420,437322,230312,846090,895322,16480,746002,846376,901662,130337,151944,208649,229419,959414,43067,971231,383437,741060,448237,771194,745411,644256,108160,892063,629553,552870,798288,244342,324740,832725,498883,20720,158213,529892,781771,843005,11404,475946,256970,449279,520209,460494,302226,357454,400053,972112,584660,485376,950350,5874,76086,407793,813441,89009,362198,786964,489896,985769,50721,526382,945033,508419,994737,366021,880781,483324,864777,962719,892541,199450,326934,980752,782405,601133,714090,355344,758171,77813,613515,685816,111781,950505,236471,665262,241366,658073,784084,560090,557818,205972,278620,15448,899816,655924,490469,881532,570507,307077,658469,330934,4526,747500,674885,268646,375820,139468,286226,924043,164730,942762,647181,558096,817069,777338,257408,419268,148403,279990,909468,437997,73537,619229,781134,662354,574193,798416,216408,106415,557138,999246,56971,508095,400516,996021,609432,474599,537905,105698,463604,631393,387625,229534,413186,684492,299078,289213,672616,756097,958413,763664,432468,960035,872570,92343,550669,946160,133746,426588,837957,61812,655611,582696,963339,853645,468095,78738,478998,864549,459320,821634,843924,68113,161264,351912,611734,827017,790019,550554,140471,961915,771973,365739,280861,373855,414047,426794,504331,675932,209100,378532,843293,458857,506869,391195,833503,140287,926350,579561,372015,829237,937246,999336,34063,274556,496135,479770,928399,760427,487273,798502,612945,762025,988445,607986,941282,280918,59035,82379,965375,42502,830498,469627,181062,156683,168683,605541,470214,418238,72938,974966,67119,154720,278714,89744,756513,417468,238378,793958,296823,355234,769209,604050,754554,810122,178051,344682,34419,532001,598854,150837,394647,920219,612370,372416,148073,870429,956476,39704,66988,129487,281159,326381,233348,542873,453917,881309,205836,716745,879353,991185,411406,910708,661005,283174,611302,427557,203936,79998,140207,372706,33404,579492,372031,418714,187901,746491,526994,129249,534134,176952,502055,472058,747024,222562,880334,381904,499538,348630,655100,622191,615215,38897,490007,737888,550465,557968,529628,592587,594243,535376,873024,838970,599478,644876,827894,684653,893604,618376,974048,484320,254838,455985,882300,14260,486326,971984,58499,766853,172064,751084,312332,240275,656479,180167,286636,992589,153846,467774,325351,179639,164185,466916,206886,402569,49089,676369,524531,953500,703891,11411,656706,966848,751874,807071,337210,558949,581712,45218,809251,770108,851110,981459,426957,10891,787594,188572,354150,758410,731672,530316,702614,448565,888109,732757,50643,866626,177785,29825,787611,851267,415640,825632,141385,796076,779459,438173,62820,257788,679750,767316,365182,961908,692739,164587,646247,634114,176510,873078,556950,379743,554558,152833,922830,783901,21572,610460,73173,511123,602972,311212,487621,946280,82767,967657,531142,337295,303561,871090,615658,975501,738003,260193,600256,180853,32781,505979,621768,246956,434252,832923,833673,44778,619030,293212,723626,684122,473410,364390,778579,488405,792233,850240,271314,550931,700798,730564,853369,309848,842719,227581,456689,904130,22096,635012,730011,554409,40153,390453,865820,850131,924489,462502,209889,618512,613342,371122,487793}

    391

    Returns: 271314

  20. 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    3

    Returns: 146893333

  21. 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    436

    Returns: 597966

  22. {247743,919262,216565,488737,718315,72316,722246,751292,122658,766473,981821,632945,635063,894072,89804,685834,179423,921608,938870,898917,703566,407921,126228,624433,115969,788537,166259,697706,517584,627495,539114,383771,881997,691294,703594,140697,263924,9186,707523,702221,949015,549839,439955,651222,697234,266483,886947,480770,377571,40972,976240,120929,843607,491737,726110,47201,857442,701467,449736,380408,233799,667400,708873,838058,146561,680420,559182,3626,716822,898755,384530,142930,584478,97865,278621,715692,154706,950178,499783,805581,606117,216690,998309,923488,549202,916955,395662,26461,431623,884869,80976,138691,401220,114688,282684,661125,358078,955050,71704,312724,353765,518334,257533,659097,328865,638538,49716,353162,419174,332879,174526,537706,706460,689,860354,341135,341412,527713,735166,35429,424439,54758,215523,219238,894229,416707,409055,339261,944474,161223,900890,969500,165948,616048,49445,530662,694107,689628,578107,550940,131664,961842,316710,144598,911073,149964,920358,116224,63643,219531,273026,986211,69971,250628,69489,276981,580697,667154,761535,599649,317035,589985,653023,437281,387318,884469,433270,33588,588822,938570,849324,464838,3346,329989,535135,797984,340570,318957,239203,219431,34966,537943,822209,156565,60018,340328,432246,708115,787803,17211,207660,149623,992470,494773,706135,886719,272901,184249,13549,991617,752887,372350,147255,377184,906362,912043,935814,738121,750776,1946,30868,620260,453440,527125,86694,366655,603673,774950,429123,233104,17856,336676,727903,665930,964988,658797,285198,591298,127118,17751,557809,578028,442004,657385,441844,904828,214642,450662,665914,888056,529799,725420,362620,307552,49430,828536,517914,405813,736892,593707,534101,729686,914111,125095,584617,33982,328365,212425,787325,572842,582109,252684,478003,367392,362272,769405,26782,457151,394726,492566,707707,717883,945101,490468,105215,559994,988928,29543,421203,709294,882063,678820,832508,315885,476597,672900,740976,837117,148013,700562,356961,497026,126047,95733,561957,637336,854761,873342,407208,944069,846583,174676,922511,358999,640563,465162,133086,466622,26874,262059,312243,285033,657575,260397,533715,683014,527930,472533,529927,95856,583055,400038,711080,818878,881468,316197,954818,920296,330077,453203,437399,734048,994433,260244,344635,968364,383563,926933,774546}

    249

    Returns: 330077

  23. 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    3

    Returns: 305774106

  24. {970443,299877,901678,592918,931069,175785,129685,261703,375823,942529,163291,100861,778432,995500,643927,765472,879914,67705,749091,991080,871409,897155,733142,250498,720043,97616,398564,114410,104539,2383,705132,111327,135291,91601,510534,926403,147863,110694,128399,978827,379398,140810,988299,773928,264177,691728,187199,938835,417563,353535,132924,519497,116837,665411,797644,942027,232937,638205,322968,22819,118870,802047,848134,549547,918563,741073,468938,249128,124198,824371,177390,408913,980568,245648,480739,23809,511743,543602,153394,104750,528377,490881,236400,702861,963191,611524,966486,278864,277731,615141,790378,278721,485210,720623,999921,164196,542289,183026,809689,690981,476886,334319,891165,927192,639606,102022,476177,361539,893178,279316,147197,463108,387247,786049,343184,223696,805155,782103,427118,538791,614847,772933,884910,764755,907801,781647,855337,427468,867866,252818,726739,851625,776185,600291,978607,430064,728852,214566,794824,358990,920748,304908,230217,927592,431963,167166,873189,869557,942518,340327,14596,859138,696560,643188,306662,965906,339013,267067,775623,769978,955621,941311,837887,883505,761624,685421,661926,824353,404783,814954,816718,544386,775254,677895,652440,427440,547783,64052,270272,241033,421002,352070,255519,351039,164068,236993,571916,490011,132661,315877,144869,507523,874383,899756,697473,824862,807821,167358,345602,766568,730087,179282,306931,547804,84357,330904,833671,459199,502001,538111,139933,709764,123080,822039,661981,463691,594562,987299,463330,838267,447330,772746,976455,17841,761056,194677,559077,182733,640307,799399,535330,652157,45725,195452,490756,496688,950895,545305,594978,888484,628523,662206,637004,626439,108791,979904,275516,598609,498297,941302,730132,425738,899691,286653,769498,167364,130187,312751,388211,765963,301340,421623,6964,854768,593011,180553,378907,661350,231204,674846,640138,1737,762430,150550,103350,778811,206569,816435,461038,973889,565661,202830,38320,851866,467825,659521,615298,987982,433538,415695,125016,768214,365730,122020,225467,215508,385678,948243,342712,350485,63437,119281,287084,807983,424554,238583,955563,99702,854057,869628,950791,738461,164246,624721,170852,420975,644539,444847,553781,603795,869652,845144,196956,100969,406658,647628,13851,782194,331945,126136,939309,56675,645888,548008,449349,590589,256047,812856,822653,625010,188929,260843,138294,336348,85920,751207,477845,912780,840691,796337,179949,407876,443431,877536,281515,976543,711499,65663,472125,798621,606593,723181,986843,851897,265309,373700,867510,709020,702949,790915,933750,701717,389712,980936,622282,120925,543894,10300,576769,602896,38508,566539,500317,489024,275698,728996,318890,741090,247635,674652,146242,943809,273033,947046,889658,33030,575230,475937,590637,650601,950762,751185,755795,445900,266603,426391,659,219176,419795,156171,302641,533344,694905,655472,39369,308526}

    15

    Returns: 14167049

  25. 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    1553

    Returns: 37239

  26. {249936,39831,59929,422158,725143,401001,148574,907766,138116,673883,458274,408934,716766,444532,697267,302766,362101,141463,813700,310889,932294,496633,438700,743513,582791,380467,175627,774955,990018,418809,702184,20330,166113,687347,360121,523908,358238,823032,21487,766700,218428,92189,540921,454188,28529,311470,30213,654645,269716,30490,524374,324344,237154,53937,347730,378004,717797,206149,634041,241154,972922,222569,6409,255654,396890,790222,380769,400449,259763,53278,220970,536686,883774,349957,344010,789655,452300,553507,550712,739582,404847,152643,940152,809113,32712,125812,755404,607424,457353,738819,3669,19179,647146,626817,895627,511155,508063,909346,356845,470157,369986,631050,478337,382931,382693,520905,793877,322082,434244,919224,698439,511602,209337,734426,155116,711401,916352,460456,77156,782340,29194,610996,417249,71556,113648,407992,47957,192448,437882,199771,975183,364530,602831,877935,290847,725392,870603,512418,541426,930371,217664,530544,865788,915074,394453,28632,338745,911724,434208,223597,446030,682384,121156,627247,511871,460408,901875,257377,202145,276064,603498,87474,934049,183075,108567,980803,137533}

    12

    Returns: 6056809

  27. 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    487

    Returns: 1342951

  28. 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    961

    Returns: 11

  29. 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    29

    Returns: 32686824

  30. 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    1357

    Returns: 371218

  31. 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    1800

    Returns: 83696

  32. 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    3

    Returns: 155646599

  33. 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    648

    Returns: 1106411

  34. 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    1671

    Returns: 4

  35. 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    182

    Returns: 4625408

  36. 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    702

    Returns: 460702

  37. 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    378

    Returns: 1119859

  38. 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    1047

    Returns: 629356

  39. 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,253093,367740,5398,731597,462832,209880,60464,989323,861975,50664,809233,871201,191521,471265,336329,411181,593049,339081,59223,899339,550453,983462,982109,890345,384028,363975,57122,300604,80007,223543,239250,174801,71670,184622,732393,871515,827405,368645,741419,742751,746606,397277,768716,863700,916044,568619,123580,6739,737375,592291,848963,847589,300678,514396,712441,341808,649453,366729,256928,316167,759240,634094,161535,582223,135055,849486,324086,298300,422072,498908,144228,881295,319498}

    242

    Returns: 2778090

  40. 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    886

    Returns: 1480

  41. 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    3

    Returns: 209516245

  42. 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    4

    Returns: 237165113

  43. 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    131

    Returns: 4814456

  44. 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    4

    Returns: 222422684

  45. 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    1654

    Returns: 143893

  46. 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    145

    Returns: 4591163

  47. 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    60

    Returns: 1839514

  48. 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    3

    Returns: 286789289

  49. 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    445

    Returns: 1702457

  50. 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    378

    Returns: 1791317

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    15

    Returns: 17468176

  52. 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    314

    Returns: 1094855

  53. 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8,750942}

    3

    Returns: 241780492

  54. 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    1705

    Returns: 133997

  55. 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    1659

    Returns: 143664

  56. 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    915

    Returns: 753272

  57. 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    552

    Returns: 722543

  58. 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    32

    Returns: 16355258

  59. {659479,282772,331900,111197,173525,328708,862042,206543,26427,337046,665902,136862,340884,934999,959606,222862,723489,222959,289489,389767,596081,748305,172252,139463,399639,840240,873997,604207,163575,693263,292141,794595,789671,13628,213811,159387,412652,876169,190132,485892,368299,678114,887870,987021,625206,722023,58257,144737,17752,11745,197352,509519,255522,303294,563131,191590,478384,316794,461579,222033,76603,286177,617352,310568,601840,700045,4170,781635,857554,170122,725912,631553,676298,853011,411461,716931,466568,746418,114649,58117,343332,482835,895250,121366,544044,951614,97774,729540,875914,194674,841869,943526,140364,541560,391506,855207,837098,876339,879632,737693,962857,261841,330845,409651,388906,885974,46691,987959,126495,440399,196509,426547,770956,593560,891318,369161,552836,178112,109072,879919,718358,77017,586655,557930,411756,563112,197338,390845,838416,23687,391966}

    8

    Returns: 7566883

  60. 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    536

    Returns: 572757

  61. 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    117

    Returns: 4096942

  62. 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11875,220304,213763,575266,608772,286768,79612,325488,380848,215005,696492,83909,362749,810777,305395,630561,863721,415105,374846,303615,115852,391203,217133,688353}

    66

    Returns: 10992259

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    449

    Returns: 361959

  64. 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    36

    Returns: 18907278

  65. 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    23

    Returns: 35430589

  66. 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    66

    Returns: 13490206

  67. 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    75

    Returns: 11522829

  68. 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    23

    Returns: 38527385

  69. 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    858

    Returns: 408973

  70. 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    4

    Returns: 22491440

  71. 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    6

    Returns: 131792353

  72. 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    48

    Returns: 19628837

  73. 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    18

    Returns: 24466689

  74. 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    5

    Returns: 155331369

  75. 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    353

    Returns: 1960554

  76. {135599,658345,950496,816968,243274,71167,189539,640143,149026,76389,213234,109815,623698,432542,519366,804370,259794,402785,910602,831800,491078,958343,96048,908792,793577,355293,248061,203368,759498,88984,981757,662666,76479,516543,768597,161712,441596,630280,495637,829538,92907,563442,738449,335745,950876,414650,328452,753646,327829,888495,964300,855359,785675,67123,942199,339736,452,351317,561454,545764,426805,239419,399235,662106,146351,148605,442535,307668,530927,925389,15428,628630,255076,40867,546238,734097,751651,721103,481886,375564,420274,424183,75654,264629,770435,142852,349775,318903,209352,985275,265725,427822,369274,366357,22777,38076,709718,928174,449327,972620,627242,466,651694,417758,458621,10763,441541,939517,572904,758610,575760,723580,213640,879473,511624,972259,874622,141314,205164,537525,770829,440425,462228,420873,400807,493033,489331,728776,287568,255279,585375,36788,732128,46595,365493,885812,817149,200096,514748,310850,957720,818540,832072,885531,12112,875473,243807,754992,337425,468631,541408,525171,203387,506245,829267,678357,662080,486815,56380,392822,312255,319032,549474,258644,393908,320920,165418,402307,302162,635905,537209,959464,919023,308373,900477,668206,127430,172470,156449,594485,494090,525207,152466,646816,385874,278630,642610,589148,719172,915653,28696,718819,132378,110318,775820,240735,618784,315592,346856,639448,560448,970488,606736,27568,663204,233141,910054,531916,508778,307626,504449,268130,312055,499672,457466,349913,999861,110083,45995,680872,912197,154524,435102,984929,267671,684499,517020,645502,31962,176708,981241,444203,981455,56604,43117,216534,563759,926875,771058,775066,622658,482672,621370,189874,177079,412829,614966,661463,222022,809915,571634,773226,953939,741873,955224,868440,913880,674102,177095,661102}

    26

    Returns: 4652337

  77. 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    989

    Returns: 33

  78. 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    1938

    Returns: 26480

  79. 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    8

    Returns: 57751819

  80. 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    6

    Returns: 145233972

  81. 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    826

    Returns: 790028

  82. 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    64

    Returns: 10964641

  83. 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    5

    Returns: 191777113

  84. 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    802

    Returns: 888063

  85. 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    4

    Returns: 157162228

  86. 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0982,812851,645593,915179,498082,610968,520684,976994,344223,128208,29898,407650,277429,717974,7791,881706,966151,40454,124009,644718,492962,659873,993039,912728,446329,547360,744985,947228,128161,139720,104421,134107,387552,187435,740166,56240,510049,614445,20880,116758,667022,7786,339749,743667,661104,156915,856043,586367,91396,270566,842188,400762,606079}

    663

    Returns: 162337

  87. 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    560

    Returns: 1124690

  88. 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    13

    Returns: 71204011

  89. 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    4

    Returns: 247889594

  90. 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    756

    Returns: 799551

  91. 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    507

    Returns: 4132

  92. 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    65

    Returns: 14209347

  93. 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    1502

    Returns: 58188

  94. 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    394

    Returns: 1130148

  95. 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    205

    Returns: 3778576

  96. 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    632

    Returns: 1078382

  97. 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    104

    Returns: 818640

  98. 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    816

    Returns: 800455

  99. 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    409

    Returns: 1684982

  100. 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    4

    Returns: 137914555

  101. 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    12

    Returns: 82404496

  102. 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    746

    Returns: 816332

  103. 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    22

    Returns: 37689402

  104. 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    267

    Returns: 3142118

  105. 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    932

    Returns: 691057

  106. 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611736,408712,30478,355009,687734,515372,920912,637636,875450,257447,692111,755596,881690,81935,132213,820293,328713,941709,928507,731411,819751,842433,644754,668046,242466,506766,259890,666188,206512,392088,838573,572026,24014,630983,369867,71649,310791,202997,932418,815133,111274,791674,122792,876614,431565,332625,118222,921839,202773,216432,835840,490822,990667,474397,397522,745604,217941,45688,512804,881761,271791,401182,451898,157181,632205,382303,996659,152768,75329,102433,129417,447096,81447,153957,247914,360706,808570,165776,379154,805578,380330,964132,205797,561474,780794,203827,715794,493224,349044,357459,939288,321646,722792,377015,546360,565688,92986,175212,45044,184520,800345,313196,941087,265655,629914,926741,499241,828852,641193,974841,680490,445403,9113,352600,420365,908557,145019,274567,660641,633218,317088,605188,449982,811666,95988,489810,988690,606961,214328,722646,708529,826809,847369,777412,350674,588042,897667,321821,533137,455517,597769,338897,483622,419110,632774,686061,454537,858612,28513,37229,834014,338724,251308,673627,120066,674977,321700,515830,734598,216288,257255,122509,119815,700983,828466,120636,681621,360535,437002,677418,922945,168847,906984,175968,544487,264841,117649,214740,381197,612219,699741,415015,789883,902648,468125,291231,506642,557265,869608,615694,52405,436274,487603,292243,480686,527530,564248,742673,633704,452405,575777,205244,101370,100864,128384,146349,762196,87529,829511,194438,125998,6698,333463,619540,695363,656613,460400,402237,216118,501939,144253,362697,996675,648293,977773,653397,441888,513774,291882,158399,569162,199864,31672,987575,552867,287664,172884,305919,277673,415344,60331,196098,472250,528801,843752,116646,241849,139902,136694,788729,721587,275327,130548,21136,131847,53923,658494,66203,733012,991571,123093,588580,48830,200003,776443,224321,256017,619608,573274,9468,822283,306138,705035,665378,315798,577410,966991,842228,806152,518404,310523,942709,430216,941874,289287,74623,505871,406401,620578,14136,42381,305000,752178,800694,618276,354745,150182,730095,375914,41520,4728,64013,316467,703892,188261,732219,169909,976228,594890,668050,861627,253560,439620,188170,623,689332,702652,4410,873837,992061,666680,38497,146925,948065}

    180

    Returns: 4552601

  107. {317861,897805,395500,773588,495272,699460,136409,847840,308357,868064,979916,453546,857232,92660,452928,438697,239388,945590,753139,635940,546022,531014,972372,516279,917722,331703,749727,257327,370366,658574,212343,312682,122575,760722,160226,425456,582845,963308,456489,41668,987468,166439,495453,248176,919624,660292,438476,684997,585525,490019,630978,363331,775259,538569,244039,958273,893978,86346,720066,939179,313347,853740,44396,850813,563662,435847,213376,164859,563814,598286,524293,384095,169288,118835,473689,500440,807619,731681,117985,483299,866274,259393,723945,206087,799649,202307,416413,106474,629901,895827,316885,919873,630592,843208,358862,25871,502601,984733,564553,303757,278576,473722,72395,905968,525133,995696,615973,27285,151335,789009,472327,572712,277443,303662,121245,608517,169707,869519,987031,618522,204989,836005,670378,881734,193225,392420,20351,737576}

    58

    Returns: 823511

  108. {111433,838600,877027,14909,435911,807572,617014,172014,22171,991859,546256,229583,10877,900053,762611,315175,263758,564939,636140,594441,944466,466027,815978,496694,81359,297501,235429,256404,105054,469162,579342,383338}

    12

    Returns: 875554

  109. {678929,402084,535005,732215,327576,263081,122065,235337,408993,788223,697408,58237,901323,134284,447154,445386,874648,753518,336668,582967,110635,182619,630621,986042,826443,706102,735157,329658,529671,219931,715618,599071,285979,883945,926226,650037,842172,570527,677438,142230,114897,692226,762163}

    13

    Returns: 1465220

  110. {436382,567557,610818,376995,977202,688349,339672,486557,298945,440715,66439,469894,247688,231874,655517,115818,95721,683458,914001,84998,118418,936759,515562,976894,393114,580683,421667,813398,162891,100253,590817,101230,542798,873418,904182,593092,436798,780026,529963,231873,280841,429237,398972,532690,630769,860243,70425,834329,673325,326080,29571,434624,454375,431435,377781,613596,990498,462733,950889,943683,458437,222424,133025,88128,341483,59273,20870,496621}

    51

    Returns: 339672

  111. {21539,151580,660740,593045,498639,325541,682795,453182,762809,814182,507326,74541,402513,923890,133134,353333,795780,99356,384366,144056,616155,698465,905979,593937,48723,151094,315404,774337,414383,73285,402419,784558,764759,155292,711617,453704,280684,545334,190468,872685,983911,10467,840886,251126,354753,371787,473319,12931,937571,583258,729784,619406,911582,351789,515891,340328,906164,380730,861770,80993,47895,159799,17987,417286,340787,721520,284866,190950,1689,937547,672317,373714,299609,737863,992105,421622,780682,101623,395681,9854,499807,790505,688019,863519,25439,573739,971592,381355,535828,128566,304462,886960,282959,890688,92613,636118,64747,876356,879038,158999,116505,901034,40703,122432,9512,679195,659428,660166,727458,5565,493832,37959,80854,590260,546875,595563,14973,148539,197174,139069,168640,30487,242140,344832,249231,16756,487132,280077,403455,903567,707179,845539,784044,153484,906495,801902,939192,198063,805844,54496,484626,944273,399000,39690,757433,658680,236877,381560,796276,681689,821581}

    3

    Returns: 23097105

  112. {122485,240430,629789,165992,762589,259525,941239,255735,865777,110990,489347,548806,904262,257586,718499,62476,140335,757708,518694,376787,417725,664080,675434,15053,125213,498641,391357,42350,128806,930258,315079,370454,348641,669562,220710,98454,442943,639171,595760,715384,753709,677759,915656,144509,267469,392860,309880,418480,849318,290011,657699,240406,419555,974764,890742,807925,59683,49303,425208,55728,258085,306860,198184,906505,635659,964779,740636,211153,527755,971078,83828,806119,741181,869498,66482,519088,653674,314517,786707,13797,578091,90488,525777,80569,974742,407985,460052,351239,662640,325669,872878,445453,654094,377416}

    3

    Returns: 14618379

  113. {890342,292932,254888,877672,637231,453751,88681,600363,637679,339406,219718,728277,361588,671454,662279,318852,227738,430746,741932,980603,781694,410461,874939,423744,56541,25965,767142,936051,669108,174597,700706,977943,662312,529352,113201,884747,968545,897437,115917,614274,639510,178076,946927,584294,664693,13417,609280,907205,283632,442310,105868,748100,186449,738720,749880,107674,892569,144895,3369,62826,899347,393979,176391,385532,900305,757573,105242,504477,486961,850809,620768,974167,268722,580843,216304,972666,272073}

    49

    Returns: 506250

  114. {813319,764430,65081,512592,778374,862935,497155,924001,388600,375448,924940,644250,83489,59619,571140,642009,108926,971241,259947,568419,764105,913108,548225,801256,30611,383968,633723,268938,483980,324613,618839,814775,971044,673946,369584,780831,525617,119951,776791,565926,390608,458789,700237,143785,816382,659847,256228,915011,513199,75363,395332,810524,249856,230315,909338,264291,111098,281612,105128,529614,353189,545166,388060,825957,630000,455257,908571,972220,601242,942671,243099,487563,579975,496419,804063,622354,928305,108400,303512,419468,368135,891197,131193,700147,238167,406287,950163}

    43

    Returns: 764048

  115. {161724,137666,963314,149932,146308,434577,316907,30198,348110,876814,974046,396187,338614,768196,720561,392566,967827,8850,388290,93047,591873,94357,518300,411133,151793,525049,82885,663887,570704,696420,357073,580889,535175,698035,957133,360062,231520,961045,396574,837932,18839,363333,249384,963917,338048,226540,155772,546561,379746,620644,457441,674231,163665,529463,207392,303571,718568,724407,663573,256119,993861,644006,146144,266781,982802,183148,314907,787443,292077,58708,506477,964824,53661,337166,759981,583734,642225,784998,555635,795225,135040,934092,92254,133692,831157,142134,137804,667812,432814,471827,101329,127260,684375,913043,995117,500477,362770,328416,382697,908331,518249,515605,241320,524326,775439,948383,906762,934100,322036,83916,913863,605248,936123,605042,597939,73108,32981,604040,780198,38934,248385,508342,724606,823990,517772,498819,824077,526372,959292,277752,150691,786982,123640,306228,87617,286864,334693,49737,749664,970200,912380,345844,794930,515579,42804,739343,531737,762724,940575,517933,933078,642678,734389,225428,285034,656530,199308,629710,716152,101058,57821,479069,781517,49289}

    165

    Returns: 0

  116. {597294,904677,848463,710073,456107,489793,831137,829798,472477,413354,856246,739985,814630,344400,532353,900332}

    11

    Returns: 739985

  117. {932916,506427,39586,810706,770242,829796,388568,106409,81841,779415,877053,316899,282158,145355,353589,270744,797970,495492,469686,558510,450319,444448,342736,658171,611536,578625,710914,183609,396566,767467,384655,504408,340152,291281,819807,638446,110073,72380,64322,628399,811540,309035,163365,579045,348943,980630,346949,154362,128563,17647,969747,611719,109488,411524,224469,385025,839824,177144,108201,819535,651481,874642,985370,908073,629137,347437,361496,781754,317658,439798,158660,267850,387128,720009,866618,43291,635745,654081,432748,784327,778271,250198,649533,241217,441311,925513,100026,351392,666615,234605,429775,345328,9702,142851,827916,296469,13504,728174,120661,719831,435360,551062,807187,633517,110560,445451,700895,963160,746793,152011,578309,291425,261213,40576,383365,732962,495487,149885,86619,149847,274063,910526,256887,13284,807033,210886,767105,964499,381347,916141,826706,530991,132760,556726,709555,513953,445800,665469,129507,278441,190142,161457,204888,549960,569190,253963,348745,349465,830278,571158,223418,383329,465801,606050,106048,545658,820705,116030,625848,187402,214158,812616,854499,460036,781849,534399,157780,351144,250262,108931,49559,995074,765370,278195,528505,463890,715625,387548,23426,522169,212704,19406,124865,763777,523386,390705,738600,139546,282069,127058,160974,131886,755781,976764,846446,735646,782228,134248,314564,964136}

    11

    Returns: 8068443

  118. {201275,464754,150753,502956,529517,434785,432484,293836,568741,938764,884001,460757,312746,679161,720289,721769,139291,827249,279049,17258,431351,114893,584558,637759,136297,474504,741615,522676,802442,885975,978809,16208,43567,758415,899627,488816,699376,999653,645384,10925,183516,907942,225781,700100,640624,157990,230829,453757,570050,447392,502199,526562}

    19

    Returns: 991907

  119. {286979,177965,770838,815256,136888,612332,582288,792565,229226,920338,631178,67177,660910,523056,265979,151498,410725,910399,612532,861020,962421,123480,486430,744229,448794,683928,467705,55018,559602,107780,851832,130293,312562,568297,500657,40374,799422,105084,582645,290893,188007,16139,813935,172300,586353,714958,90005,76700,856487,386601,332307,731644,103096,234610,965081,836617,356291,974940,684595,30362,917841,503578,86402,465792,946737,341256,275765,524149,122588,541706,802213,361175,644357,239140,131294,45478,397077,906155,394860,22869,850696,695015,345843,520354,142836,943272,284258,289595,841248,38958,218271,782038,81897,361060,677463,446516,135083,937778,405021,345057,964702,798055,621377,693728,14665,731131,673909,252741,281731,314382,665629,713684,715421,621463,90349,361605,123389,980773,592651,325842,54576,518545,718039,675831,582667,991324,921984,466807,518788,589404,166145,595144,345136,975778,145849,984260,80113,814404,565018,189361,360776,437119,903012,982949,259844,100285,802463,862895,742194,490242,547969,711020,209735,750925,102600,22488,283740,327496,822491,224981,830152,346604,279350,611469}

    135

    Returns: 151498

  120. {194688,332569,246573,623799,300743,48658,815706,474791,800763,867662,616882,961206,779136,336201,321826,766476,415739,733800,471188,246669,620655,546804,904447,48524,538098,357095,630977,457551,664313,988293,889525,825219,743189,241378,15370,491649,178491,447176,262785,593854,433101,364928,914996,29455,773308,664137,854624,631938,760172,341177}

    12

    Returns: 1840242

  121. {283634,469287,743678,394164,247122,654814,912928,566451,615753,533271,849232,449543,809188,939585,595465,951803,946088,705495,550416,891900,923520,232934,949761,710070,360436,778203,642187,789179,676827,359464,989452,46643,983541,48681,325583,634985,517278,164031,173121,171854,71104,539943,333263,909559,242918,619301,41953,649695,352595,585978,615408,10193,563129,135760,396271,860126,81886,769841,355521,351875,315191,687458}

    3

    Returns: 10962006

  122. {688942,667958,616773,295935,303644,686186,383325,920559,958520,894695,231465,511345,393100,946818,122670,180424,196538,547086,557316,490088,960105,295036,277884,921497,327093,112475,859626,454138,179291,632273,777978,644359,875948,486336,796849,854022,544173,646235,683066,699242,908944,842033,319657,364390,46435,613177,264236,157970,746110,729881,678701,574702,875052,564265,342524,172037,252245,487558,154359,769589,61035,523035,125261,836367,754766,293875,371755,443397,743573,770994,28076,828285,889591,447957,314317,443453,983349,348384,220837,341216,925840,705859}

    39

    Returns: 815152

  123. {885810,82665,370143,756645,227633,243476,351279,3154,426326,355990,901329,169960,874119,235197,454325,644602,114215,495517,936283,397136,826691,436775,833798,203829,914319,174504,377742,657855,942582,731999,813679,249367,474339,355518,344823,794401,31950,14198,353906,145376,518312,902723,937060,425533,933145,777443,615833,995472,131991,125634,332725,982016,192775,492729,481115,477961,678416,773858,772229,455826,713849,913660,199808,29538,331956,252353,227365,945085,985287,706166,593464,84448,469095,76743,807191,326726,756060,46791,488991,326175,404257,838206,201325,638951,267260,84080,309077,158671,208940,197488,711435,5485,405374,407588,994945,854149,602443,677556,671711,183681,390037,919061,687231,84498,152473,274422,309088,68491,859556,750296,840756,793327,273904,155684,344014,734339,467481,122238,698979,615671,763978,966304,882535,846931,353502,289819,303914,302414,862222,511146,400487,527033,101959,967089,467286,856423,73369,833830,870566,998234,51241,877165,378715,337462,241555,961410,333067,600751,67356,321522,776704,542885,614087,834415,461064,3287,144962,913172,858208,21164,883046,191786,920822,694975,449120,868245,352580,125267,443025,430248,578213,89449,661077,500518,435659,62926,353266,707622}

    6

    Returns: 14352298

  124. {409790,150824,742490,809644,764242,79327,473313,334007,325558,729727,644693,549792,490171,21466,400841,583562,971008,447604,504194,721668,455707,665350,22833,829143,904150,867753,838214,873463,286011,774614,358352,10816,454505,608973,795272,424036,154288,610112,245393,988982,869501,474814,597665,890137,332132,615722,986645,506378,31477,278926,106338,244309,992139,372504,205525,509260,421093,323549,996398,672988,563554,403278,25752,722311,252912,738174,281571,254358,191745,659623,937757,621812,958952,135399,175881,325462,102270,773349,965197,201586,445976,291019,530825,558119,920333,404464,994862,176268,802307,805375,336331,13175,246407,267664,383256,516421,379944,953004,23780,692618,38797,669392,203131,460027,427776,177601,559373,359082,603931,637477,743254,394897,701650,939349,566119,642287,245165,975399,124693,256515,727094,871633,962736,701929,870869,823211,146894,335859,640474,454165,857736,966561,112592,557136,726849,641727,784356,659571,686979,717993,754072,109888,544610,212095,482864,280448,832980,540748,521885,43732,758452,19046,672809,893942,214244,906092,538506,958331,902958,361795,316380,670862,582921,410188,988562,65391,333305,892344,771162,486371,519045}

    47

    Returns: 1585797

  125. {543279,39291,359658,257691,384436,285770,220602,877366,99433,937028,551086,859449,756966,780540,151939,128106,663622,953186,162652,984255,553740,360141,342392,451395,174325,914860,550111,186141,780557,496774,961234,407207,827921,926680,407088,903068,323774,319334,978081,941197,884139,888602,692788,820738,530808,652593,602481,885641,659309,514498,174279,46786,410086,879456,175956,249247,883206,308573,571615,864855,251220,708291,129775,690381,845250,206632,544085,88101,716189,177398,871749,818236,5866,839245,5869,281656,702314,478615,715321,216474,998770,623814,509381,373580,527802,432120,214231,333865,199964,142606,684581,423831,240639,694441,516046,636476,289230,513756,972540,570792,101626,31717,597830,665911,479888,712289,141536,424868,542315,240232,497234,898161,342622,48182,323960,428715,148654,546267,902292,547579,399130,258499,562319,953596,471103,567278,713199,710514,911401,920636,102615,151425,712006,166461,439360,493139,542384,143704,923377,832015,591009,782710,544983,18003,813844,745071,238638,885063,939296,68012,106497,453836,537173,369120,963121,16406,823423,914308,395091,463138}

    134

    Returns: 206632

  126. {249541,201849,247631,712088,85009,611974,485058,441720,748781,851080,339257,337301,744847,804750,788847,394789,394584,10086,720935,513961,512077,813544,492951,229253,52763,459624,235235,519869,966773,668194,350799,142145,915063,567780,673637,939929,339463,817986,658017,757598,617023,376276,788625,905610,674540,642670,125034,609868,490901,650465,523865,513911,372902,561938,618146,96877,754450,975035,75737,820364,539563,450372,7344,923804,686336,227468,649518,50597,812063,314910,609162,306261,88957,11268,23474,925004,595406,441852,962845,452585,589474,881007,284170,241040,879362,470447,928108,94766,579804,441202,346253,107676,63863,100076,342774,87566,846381,651072,120007,476549,468312,388083,728565,345330,190452,917192,439957,864328,450569,845265,783330,636047,589698,806083,117795,410847,311394,786070,648000,2173,701950,458770,732922,667509,410143,640518,186535,827766,761796}

    8

    Returns: 8055048

  127. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000 }

    6

    Returns: 5000000

  128. {3, 5, 4 }

    3

    Returns: 3

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
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