TopCoder Statistics - Problem Statement

Problem Statement

Alice and Bob are playing a game on a graph. The graph has int N nodes, and M directed edges. The graph is described by the int[] from,to,cost. The i-th edge is a directed edge that connects node from[i] to node to[i] and has weight cost[i]. This graph may have self loops or multiple edges. Each node has at least one outgoing edge.

Alice is currently at at node 0. She wishes to travel to node N-1. Bob initially has K tokens. At each node along Alice's path, she will first announce which outgoing edge she intends to traverse. If Bob wishes and if he still has a token, he may spend one token and choose a different outgoing edge from Alice's current node. Alice will then be forced to travel along the edge chosen by Bob and incur the cost of this edge. If Bob does not use a token, Alice travels along the edge she announced, incurring the cost of the edge. Alice knows how many tokens Bob has remaining at all times. The game ends when Alice reaches node N-1, or she traverses an edge 1,000,000,000 times without reaching the node N-1.

Alice wishes to minimize her travel time. Bob will use his tokens in such a way that Alice cannot reach node N-1 if it is possible. Otherwise, he will use them to maximize the total cost that Alice incurs before reaching node N-1, and Alice will always choose an option to minimize the total cost. If it is not possible for Alice to make it to node N-1, return -1. Otherwise, compute and return the minimum time that Alice can guarantee to reach the node N-1.

Definition

Class:: MaliciousPath
Method:: minPath
Parameters:: int, int, int[], int[], int[]
Returns:: long
Method signature:: long minPath(int N, int K, int[] from, int[] to, int[] cost)
(be sure your method is public)

Constraints

N will be between 2 and 1,000, inclusive.
from,to,cost will each contain between 1 and 2,500 elements, inclusive.
from,to,cost will contain the same number of elements.
Each element of from,to will be between 0 and N-1, inclusive.
Each element of cost will be between 0 and 1,000,000, inclusive.
Each integer between 0 and N-1, inclusive, will appear at least once in the array from.
K will be between 0 and 1,000, inclusive.

Examples

3

1000

{0,1,1,2}

{1,0,2,2}

{3,2,1,1}

Returns: 5004

When Alice is at node 0, she will attempt to travel to node 1 using the first edge. Bob will do nothing. When Alice is at node 1, she will attempt to travel to node 2 using the third edge. If Bob has a token, Bob will make her go back to node 0 instead using the second edge. Thus, Alice has to travel the cycle 0->1->0 1000 times before she can successfully make it to node 2. This will yield a total cost of 5004.
4

1

{0,0,1,1,1,2,2,3}

{1,3,0,2,3,2,1,3}

{0,100,103,0,0,34,102,33}

Returns: 100

In this case, Alice's optimal strategy is to attempt to go to node 3 directly from node 0. Bob's optimal response will be not use a token, allowing Alice to reach node 3.
10

5

{0,0,1,1,2,2,3,3,4,4,4,5,5,6,6,7,7,8,8,9,9}

{1,1,2,2,3,3,4,4,5,5,4,6,6,7,7,8,8,9,9,9,9}

{2,10,10,1,2,10,10,1,2,10,100,10,2,1,10,10,2,1,10,10,1}

Returns: 514
50

200

{0,13,8,17,3,8,4,21,11,20,2,18,21,2,4,9,17,0,14,10,15,18,1,22,10,14, 19,24,5,5,12,7,7,16,19,13,20,15,23,6,23,9,3,6,16,11,22,24,12,1,25,25, 26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37, 37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48, 49,49,37,9,14,0,33,20,46,26,12,11,2,7,34,19,37,5,2,17,41,16,34,13,18, 35,6,14,16,25,9,10,5,10,7,36,45,3,6,22,32,28,45,40,16,36,28,16,34,1, 9,19,18,6,15,29,12,5,44,33,49,14,40,1,30,21,37,49,1,44,42,6,38,1,31, 40,37,34,35,6,43,29,41,48,17,4,38,26,4,46,43,6,27,30,0,16,40,33,0,42, 41,10,33,47,11,37,49,25,36,20,47,12,28,17,11,17,26,26,37,34,27,17,8, 2,13,43,36,28,1,23,29,40,18,22,0,7,30,23,3,39,5,23,28,38,44,19,43,15, 16,43,5,27,24,25,7,16,38,33,33,1,9,25,47,0,31,30,29,4,36,49,26,6,39, 40,28,39,48,26,2,15,41,42,32,0,35,34,28,30,40,3,33,16,15,41,45,12,33, 35,16,47,34,23}

{41,42,17,0,2,7,28,32,31,33,6,42,11,13,7,40,47,21,4,6,19,15,4,18,30,25, 2,10,30,34,1,47,35,23,3,0,9,25,42,21,4,6,47,32,5,40,5,0,8,49,16,29,8, 11,42,33,35,26,27,43,35,6,14,13,44,25,13,42,2,26,17,3,40,31,18,12,24, 37,0,37,15,44,35,40,10,1,35,47,36,33,2,39,23,28,32,0,6,21,33,41,0,19, 16,29,35,16,44,6,18,17,2,46,41,11,27,5,44,1,48,15,43,8,41,33,16,11,45, 47,19,41,14,41,8,24,13,3,44,41,42,30,31,44,21,14,43,48,0,6,25,38,36,14, 36,22,43,15,20,19,37,25,17,44,17,46,8,25,33,19,42,40,42,24,15,31,34,8, 41,25,20,29,2,5,43,28,33,40,31,27,6,21,9,35,8,8,26,13,11,31,4,4,30,34, 35,1,15,11,10,24,15,24,23,16,24,32,9,1,6,17,48,6,35,19,12,5,21,23,25,9, 17,47,19,23,22,35,19,5,1,10,9,41,11,45,0,23,0,11,39,0,17,2,18,4,17,24,0, 10,19,4,36,22,42,18,13,48,27,11,19,28,31,39,32,48,2,26,38,43,38,49,34, 37,11,9,11,14,12,9,37,0,22,14,15,0,8,23,7,43,5,8,16,47}

{494,848305,3326,6008,223,2,6,673,152335,25,713909,42842,122,9941,361853, 35,20157,1098,41,83693,365851,43843,622,591230,7722,2489,7,861622,21272, 169,1153,3,7,3,577031,24522,5,241,757900,11036,8892,199,7,2,1,453031,115, 13,125,67,35,91,33427,14,106,203749,5,1804,4543,23,1,281,441212,18,3, 11629,233,388188,10,701,76170,763,875,11606,44972,6449,37409,83516,5912, 6,705899,26759,253,580531,14215,21916,884775,30,678,5940,17,480830,8, 61,218613,683352,4,557589,2619,3658,221515,15825,163577,25,9,1,4,13,2,88, 147,110163,18118,2,15429,211872,24,1,188382,12500,2348,190,4279,40,8428, 56325,933152,231523,9454,21,4855,96168,1722,329515,77,1,3,3518,10926, 12172,4,71,181976,1318,9,5086,905,108490,80164,2,10236,197,1880,17420, 614650,372457,13918,36,17,167,6,254127,512,15,341436,1,186,96,7,3,42,4, 3,4,492598,18523,172302,1,421535,390382,2952,6228,871,505372,131266,5, 743902,11,34,657,4717,3196,259,192504,229,6786,28,44364,21123,8,166781, 885021,2,828,497,376,24707,52,1,1659,19402,27261,82,473,443,1089,586,20, 7,239277,27132,4681,761,10644,17798,1,820306,13330,19,293167,2,4,89279, 14,1,9,18023,1165,495221,32304,538,178613,1,4764,32767,114,103,1,302,428, 92,927352,22270,2646,3599,6,16362,3,4,280286,338,652,2,347022,23,323084, 3338,46,58,1263,93,46992,19112,1,19499,33,807600,20296,16803,911294,3151, 1,793,1,1,504,62209,1397,52726,3650,54,3630,358480,178,394,28,137436,52764, 1209,1599}

Returns: 121213509
20

1000

{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,18}

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,0}

{1000000,1000000,1000000,1000000,1000000,1000000,1000000,1000000,1000000,1000000, 1000000,1000000,1000000,1000000,1000000,1000000,1000000,1000000,1000000,1000000, 1000000}

Returns: 19019000000
2

0

{0,1}

{0,1}

{5,4}

Returns: -1
833

1000

{608,543,495,257,789,263,744,447,151,423,396,431,498,676,379,378,526,105,576,249,449,192,90,217,731,140,123,19,598,237,162,649,822,389,76,96,271,366,33,570,60,342,318,774,555,725,171,720,787,339,307,287,399,494,679,786,580,732,64,131,289,351,800,635,273,203,553,519,528,619,400,749,764,747,621,799,822,335,752,494,312,105,425,573,820,624,46,208,141,829,805,180,631,563,544,699,183,637,185,802,536,110,42,229,410,603,29,42,793,741,131,626,129,759,547,646,694,582,786,266,247,811,569,578,656,308,252,485,136,138,134,8,328,309,561,439,236,581,784,761,779,629,486,209,285,167,550,578,485,540,349,639,205,81,594,496,410,430,668,495,174,362,387,801,127,221,87,602,52,683,49,336,318,296,270,40,344,141,599,371,649,591,220,184,648,606,501,560,348,620,405,92,177,187,102,500,151,290,144,346,632,794,98,472,267,57,384,223,24,24,438,118,788,271,708,456,777,303,773,101,444,483,452,16,32,149,86,406,325,797,459,440,176,122,392,224,656,524,179,450,615,400,831,430,562,797,184,759,495,248,353,179,448,730,217,488,558,109,590,467,71,357,617,182,640,454,471,189,457,444,604,316,282,407,282,747,645,37,596,374,653,445,50,314,211,150,625,54,172,205,244,643,248,657,700,608,75,521,405,484,372,458,379,652,37,639,739,169,304,683,96,115,706,633,692,715,158,123,47,643,596,655,520,479,465,536,796,84,54,697,433,108,413,702,390,386,794,364,611,372,420,193,763,492,468,332,530,317,259,616,438,125,171,181,204,577,110,261,103,135,211,103,780,377,57,733,778,375,94,270,483,546,529,469,818,520,370,745,676,434,806,513,748,14,458,757,288,535,714,742,568,616,727,106,775,461,51,173,210,20,415,474,733,710,23,468,765,627,263,499,594,632,678,239,212,337,133,88,241,434,428,274,372,343,629,27,368,130,763,572,732,100,124,586,677,787,362,827,671,380,704,334,352,454,403,538,643,215,505,241,612,657,570,329,135,51,65,163,272,47,817,773,687,347,239,140,315,473,555,409,21,695,784,51,350,713,269,118,439,229,348,56,70,369,191,499,556,675,821,745,554,186,754,544,78,504,556,376,383,551,142,533,172,277,613,518,331,455,560,427,526,583,326,516,220,66,693,414,636,529,337,135,531,338,503,442,753,684,600,746,44,457,360,238,321,283,449,126,365,521,596,231,531,272,760,508,735,272,83,717,735,591,617,220,148,7,308,73,82,749,456,222,227,207,81,741,409,767,275,257,139,225,428,398,768,553,450,35,791,260,250,88,264,155,59,497,486,45,403,307,125,206,44,142,487,219,3,552,63,467,25,97,112,638,791,605,169,290,213,11,296,371,781,421,506,64,734,300,601,746,724,13,16,19,359,113,263,426,114,750,405,268,164,146,723,71,187,603,688,825,684,677,244,34,315,32,218,827,167,579,270,340,566,400,180,161,475,762,798,505,6,726,62,469,431,189,594,514,433,586,376,131,743,15,417,442,150,70,408,312,196,696,446,300,681,375,382,592,762,74,479,126,490,327,404,790,719,517,1,691,380,436,90,488,557,804,828,385,344,671,513,718,8,140,720,485,68,582,513,378,733,361,685,497,137,493,77,807,462,748,726,625,255,532,526,669,92,370,282,748,95,712,203,283,7,668,5,3,306,5,780,49,607,507,104,208,345,693,85,156,286,470,423,197,124,175,219,236,129,437,737,307,242,186,587,25,119,480,419,341,532,299,340,132,120,42,166,268,394,351,774,421,196,216,737,636,492,635,552,540,59,349,577,83,80,734,539,138,254,662,134,664,238,810,129,613,316,41,682,569,6,115,60,202,457,213,418,399,509,176,470,295,654,89,562,227,451,92,661,426,493,228,254,721,482,119,454,53,587,326,30,112,673,335,550,562,196,560,246,388,731,716,166,664,38,742,9,292,152,609,481,367,417,799,500,279,816,789,398,717,776,252,323,88,161,79,221,404,566,297,93,361,464,22,322,702,310,651,755,825,20,630,420,542,94,159,829,610,121,657,284,727,726,636,452,534,439,740,511,816,618,281,125,53,512,393,222,488,419,808,568,655,603,74,704,558,663,792,538,21,581,402,619,19,506,177,157,813,202,14,797,525,16,651,96,705,702,719,215,676,764,464,714,774,641,626,672,790,1,7,524,699,106,684,383,642,779,432,325,264,618,743,342,391,292,79,391,525,632,266,522,677,233,575,529,26,337,810,99,818,305,478,667,548,601,434,699,777,142,365,524,783,609,686,424,788,228,481,145,481,706,36,753,425,407,689,62,427,195,798,215,627,394,709,674,358,818,407,280,527,810,63,111,438,628,588,353,322,756,565,516,704,31,541,708,116,72,110,207,520,188,69,480,510,658,612,538,518,769,89,383,703,522,163,13,6,277,334,194,301,377,420,368,144,328,725,503,353,563,234,525,77,289,313,0,611,210,259,659,743,85,606,98,444,589,787,512,725,4,29,418,225,199,75,831,453,762,812,193,462,250,580,771,316,233,113,689,17,412,305,670,658,441,422,519,201,595,162,714,584,739,173,572,464,468,515,262,397,332,504,58,648,615,4,478,436,168,21,76,722,593,235,679,294,474,133,97,696,515,340,61,759,74,533,792,765,82,479,35,297,114,397,309,490,357,584,240,489,437,623,393,156,67,455,675,289,226,143,623,585,641,629,489,170,324,364,543,5,184,396,660,388,579,570,343,146,153,417,766,711,326,210,25,401,12,267,807,390,565,242,382,736,645,232,491,12,790,590,221,447,512,73,796,828,198,549,251,147,625,484,154,688,697,534,761,545,342,471,86,204,166,261,377,515,303,811,165,745,581,429,778,93,749,165,59,395,265,192,323,311,291,549,421,545,130,785,365,557,681,168,803,817,681,275,23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26,124946,123690,657446,999198,999754,999338,123754,657176,124978,655446,656111,655081,657406,999798,124484,655231,999868,655821,124652,124384,654801,999953,999238,657186,999278,999679,656031,655351,999442,656656,656721,999597,999735,657346,123696,656231,655426,124582,655416,124030,655366,655411,123854,999596,999178,656036,123642,656806,999882,123548,999245,124564,125092,999403,658006,123838,123550,999539,654861,999527,656501,124376,999175,657821,124022,657971,657816,124208,999391,656811,999603,999410,657651,656441,999544,123996,124296,124806,999665,124884,656826,124544,124780,123786,655746,999321,658096,123556,655721,657171,655626,654621,999881,124070,655206,658356,655916,656356,123810,124660,123964,123878,125012,654631,655961,654946,657851,999971,125094,656316,124268,123698,999565,124482,124870,123464,655216,657271,124618,999832,656496,999677,999571,655286,999472,654406,999506,655196,656631,656986,654851,656181,999686,124462,655756,124392,999270,999633,124708,123596,657866,655036,655951,656661,999213,656651,656841,124448,124764,123814,657976,999852,654871,654401,124332,124038,999550,999510,999622,655171,655346,657206,999297,655876,999194,655611,656056,999789,999760,999501,124388,657081,123484,999595,999477,124734,656156,999926,999451,656946,655191,124092,999532,656976,999508,124628,999507,658246,124580,123666,125076,655586,124980,124126,124200,999605,123908,124612,999807,124120,999355,654751,124920,657461,999494,125088,123752,999635,655861,999275,658371,124456,657326,124874,999962,657691,999644,654971,999847,124468,999229,654691,655241,999796,999937,124682,658186,123508,658241,655751,655331,999349,123944,999634,123744,123638,999257,999914,123458,125080,124130,124524,655636,123984,124528,658311,124878,657521,123922,124276,124002,999877,124496,124166,655956,657101,124014,124702,125040,999919,656266,655691,124072,656696,999959,124668,124202,999461,999280,654951,654436,657251,999974,656956,999895,654566,125028,125036,658171,999303,999486,124728,656551,124614,655321,655576,124634,999366,654446,123994,657966,999309,999687,999567,124424,999993,124656,999699,657546,999256,123740,999940,124068,655176,123800,656191,999431,654896,125026,999344,655136,123902,124402,124740,123686,654931,125070,655431,999469,999646,657311,124250,657746,123476,657666,999498,124594,124440,124034,654741,999723,999531,999814,657006,124472,124224,999581,999625,656626,999252,999874,657721,657246,999992,999615,999801,999628,123704,654826,999968,999896,999871,124992,657086,656836,656281}

Returns: 93855305784

This should hopefully break optimized Bellman Fords (takes at least 15s in Java, so C++ will probably time out too).
7

3

{0,0,1,1,1,2,2,3,3,4,4,5,5,6,6}

{0,1,2,5,6,0,4,0,4,3,4,5,0,6,6}

{0,10,1,2,8,10,0,10000,0,0,10,0,100,22,33}

Returns: 10141
664

837

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Returns: 832778486
881

578

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Returns: 503365375
697

327

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Returns: 320299268
6

1000

{0,0,1,1,2,2,3,3,4,4,5,5}

{1,4,2,4,3,4,3,2,5,0,0,4}

{1,10,1,2,1,3,1000,0,1,10,23,10}

Returns: 997007
6

2

{0,0,1,1,2,2,3,3,4,4,5,5}

{1,4,2,4,3,4,3,2,5,0,0,4}

{1,10,1,2,1,3,1000,0,1,10,23,10}

Returns: 30
6

1000

{0,0,1,1,2,2,3,3,4,4,5,5}

{1,4,2,4,3,4,3,3,5,0,0,4}

{1,10,1,2,1,3,1000,0,1,10,23,10}

Returns: -1
710

377

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Returns: 644360364
924

956

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Returns: 1891051820
783

41

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Returns: 73779398
594

978

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Returns: 2304119365
786

757

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Returns: 1843400853
400

687

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Returns: 1014591705
485

127

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Returns: 126324995
353

876

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Returns: 876075689
351

869

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Returns: 1101590868
490

920

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Returns: 1341273457
66

886

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Returns: 881368758
53

234

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Returns: 234266382
84

775

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Returns: 790493602
53

858

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Returns: 857497655
57

986

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Returns: 983848879
1000

1000

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Returns: 999999000000
800

153

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98,999341,123614,999395,124778,658261,999794,124742,654386,124192,999287,658186,657031,124262,657471,656146,655996,124230,657721,999690,655686,124522,999366,123992,655091,999556,658121,124320,999359,124218,999255,123810,124924,658241,124468,999294,999892,124926,656476,999732,124680,655081,124788,123490,124594,999218,999210,999503,124476,123954,124426,123460,999357,999693,999754,999666,123668,123536,656351,123744,999280,123456,656551,656786,999349,657466,124696,999816,123682,124490,124060,123464,124384,124300,123758,124616,999958,999624,656581,123524,124878,999308,123722,124390,123736,124446,657711,123574,656756,657581,125042,656711,124012,123862,124670,999724,655591,655421,999371,999902,999412,656441,124588,124214,123840,656161,999631,999448,654321,999607,657526,124612,999923,999228,999542,656771,655676,655741,999745,999281,123940,124836,124116,999674,654671,124536,657886,999384,999763,654421,999802,123754,123818,657111,999523,999406,999791,999723,124472,999998,658206,656431,657621,124848,655506,999742,999960,655936,999424,123592,657411,655521,999263,656371,124486,999322,999346,654991,999749,999780,658106,999621,999343,654896,124648,123530,123470,999986,124758,123834,999605,999224,999429,657791,999785,654926,654761,999712,999661,999555,124170,123588,999863,124548,999826,999838,656021,655076,656136,999954,124424,123558,999345,656421,999296,657681,123606,124420,999912,124754,999668,999803,656821,999934,657126,657136,123596,124328,656121,999302,655266,999980,124888,999246,999582,654721,123734,999632,124132,655606,999924,124396,999620,654581,999815,999670,999546,658171,656166,999238,654556,999240,124636,123830,123888,123804,999237,655656,124240,999911,999955,124626,124050,658061,654586,124330,657946,123904,123930,999875,124560,655671,124186,655511,123640,655571,124108,123790}

Returns: 13401650817
939

27

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Returns: 11796007
645

954

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Returns: -1
824

119

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Returns: 56547381
527

874

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Returns: -1
430

0

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Returns: 226392
807

0

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Returns: 1325662
840

0

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Returns: 1613047
354

0

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Returns: 451867
293

0

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Returns: 453947
910

1

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Returns: 2328503
857

37

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Returns: 52423673
936

982

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Returns: 845626060
910

335

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Returns: 459686882
890

287

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Returns: 467150496
433

567

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Returns: 634491784
384

612

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Returns: 650461081
308

351

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Returns: 338820821
308

797

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Returns: 885287529
119

42

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Returns: 39322135
172

357

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Returns: 348084361
130

514

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Returns: 502443152
144

14

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{22,125,32,26,80,139,0,134,18,118,57,91,120,79,53,85,123,76,101,121,54,122,124,53,87,76,118,34,30,37,113,36,123,92,122,72,30,23,96,28,141,56,77,103,93,5,119,40,114,52,68,33,137,75,103,52,56,17,56,93,131,23,24,130,55,75,79,100,69,116,108,66,106,97,65,105,105,71,76,91,89,104,76,44,30,69,101,88,50,24,117,80,14,11,141,39,45,16,44,114,25,2,8,95,104,103,44,70,49,23,89,127,123,106,76,100,34,61,136,90,84,44,66,0,74,116,27,114,131,107,30,0,132,97,119,27,88,27,23,94,121,28,3,72,128,49,39,47,72,58,127,20,78,79,87,129,115,8,1,9,40,0,100,73,93,143,3,7,103,130,58,142,119,41,96,110,10,126,122,112,15,119,106,142,27,89,55,72,34,124,118,32,84,10,100,13,61,22,67,53,31,32,61,123,110,12,140,137,27,127,41,95,109,92,45,94,70,22,51,136,108,125,99,130,65,112,118,53,120,2,49,40,75,78,109,110,46,31,51,128,133,53,106,66,103,12,81,71,140,134,60,122,121,142,4,72,70,74,68,117,112,120,77,59,9,34,111,140,9,51,49,48,50,9,60,139,36,117,51,22,34,23,138,70,80,43,87,110,75,68,78,34,135,37,74,107,32,3,86,136,56,96,46,33,44,18,107,38,34,68,8,1,102,49,137,33,84,71,142,12,12,112,49,80,23,118,110,49,11,98,11,120,79,104,86,107,64,83,130,3,49,91,70,67,135,31,6,61,5,114,32,61,27,36,99,124,55,108,82,16,77,26,58,92,127,7,124,55,24,100,43,20,25,87,99,80,22,128,59,127,139,139,134,75,83,66,21,138,129,57,13,138,17,140,38,101,60,97,94,132,17,120,120,142,98,108,121,75,6,127,108,53,75,73,3,46,2,43,47,48,11,91,96,112,135,82,61,110,5,0,62,18,66,33,131,128,49,32,26,7,63,142,13,126,57,21,127,72,143,38,85,80,20,0,137,6,37,7,28,81,64,13,122,27,101,27,68,117,19,77,75,13,109,44,8,92,55,15,27,67,92,137,77,19,30,24,90,110,51,26,106,128,65,112,56,54,26,79,48,74,119,119,97,124,8,16,4,50,80,16,125,37,4,44,81,72,135,47,63,76,35,89,95,125,12,96,96,8,38,131,61,94,0,81,48,35,142,86,124,64,65,50,23,65,5,60,103,115,7,137,83,13,38,127,115,109,112,50,6,17,48,92,87,81,130,91,87,137,35,98,113,32,43,116,73,69,133,49,122,24,134,129,22,104,38,98,38,141,44,22,26,87,27,102,99,63,20,108,19,100,65,53,19,29,92,50,116,79,27,140,131,18,134,68,32,20,65,54,89,76,140,37,1,125,33,85,15,5,123,102,58,1,0,47,107,23,72,72,141,92,118,131,21,22,9,127,128,93,112,33,30,39,72,103,99,141,43,132,67,52,129,141,96,81,104,18,24,72,3,90,129,46,98,15,128,43,79,48,12,33,123,55,43,94,28,35,50,130,37,129,39,83,111,124,7,49,125,119,59,34,70,83,108,112,7,80,32,16,61,115,50,25,80,82,56,82,46,128,137,72,39,10,38,53,48,105,57,131,5,26,21,85,46,71,2,66,71,142,138,87,52,119,115,30,24,60,52,133,49,82,90,4,41,4,2,27,125,54,54,43,92,12,22,115,44,51,105,69,43,63,47,133,100,42,84,107,110,103,70,130,139,28,81,80,57,88,143,48,65,114,96,38,24,69,75,32,139,127,140,69,65,77,9,111,43,22,75,100,28,77,48,24,141,77,80,126,48,113,68,38,141,126,65,81,51,103,80,96,38,27,91,60,69,0,20,126,44,108,76,25,117,135,24,88,135,129,102,120,9,137,136,90,64,93,109,36,5,141,43,118,7,117,128,82,2,135,86,127,89,51,82,14,95,132,88,72,43,121,49,26,57,47,131,63,111,105,84,83,77,67,83,44,95,67,124,28,3,12,20,12,16,37,41,108,126,110,11,17,63,136,57,2,107,110,117,123,5,4,62,68,50,11,140,5,55,110,12,86,109,36,85,66,73,120,95,134,56,101,137,95,53,32,12,118,80,114,140,68,82,39,34,125,15,29,137,109,17,74,45,80,134,30,6,2,56,119,115,11,142,0,134,20,39,123,88,124,27,107,106,21,99,10,44,101,115,46,64,9,24,117,31,94,28,96,58,44,2,126,117,103}

{2,320,397,1,9,44,1,1,5,87,1,1,24,920,5,3,105,25,278,1,44,337,3,1,4,80,165,186,33,244,283,69,331,304,9,209,128,874,6,1,3,189,4,69,661,320,442,16,2,92,6,2,2,1,7,174,162,36,55,10,191,234,3,27,1,42,34,13,17,4,314,58,290,472,251,683,3,1,1,23,69,42,526,31,24,206,5,14,25,183,119,6,47,19,169,1,3,9,648,371,1,470,25,661,8,28,103,1,2,1,22,3,431,65,306,2,2,35,881,49,9,1,30,160,9,55,60,24,1,234,409,466,13,15,58,3,7,916,4,1,4,27,32,43,1,25,2,150,19,7,719,1,135,30,58,1,38,3,21,2,131,1,4,129,555,1,504,5,5,755,97,6,411,6,759600,2,830,67,130,3,4,182,915,3,70,160,21,26,59,134,7,66,355,205,116,410,11,64,15,2,10,50,212,2,9,118,31,1,280,18,7,6,68,126,756,3,99,643,356,1,8,872,717,104,179,10,39,910677,380,675893,419,10,744849,2,2,127,492,161,6,41,11,18,81,82,5,23,5,1,3,2,218,25,78,49,1,1,178,80,146,304,5,4,5,1,11,7,25,19,415,1,694,6,26,346,20,427,234,418,11,323,6,35,14,2,20,176,20,1,296,2,97,494,1,12,401494,979,116,33,1,1,276,4,26,181,29,823,195,46,160,32,18,117,35,8,73,81,22,3,5,44,62,11,37,303,4,55,7,121,714,5,74,166,547,1,344,4,495,152,1,7,32,7,49,431,62,196,154,3,13,12,593,28,1,578,2,94,2,371,18,74,1,8,1,1,164,2,65,10,1,1,67,204,11,2,33,487,20,512,21,160,6,27,12,622,38,288,3,693,69,34,385,51,957,57,80,15,4,4,2,860,2,10,3,18,421,24,24,1,2,346,440,32,26,96,632,2,16,23,23,497037,175,16,244,1,2,1,287,192,368,12,358,2,487,1,13,11,2,1,895129,146,14,1,1,10,160,3,647,119,14,12,8,188,1,1,9,98,747,19,332,293,6,1,48,69,2,713275,95,74,7,80,24,24,35,114,40,335,4,802,34,648,6,882,24,351,487,829,1,196,46,2,20,9,197,38,10,14,539,109,323,8,23,16,375,2,1,114,24,431,584,2,1,39,186,72,88,232,1,1,165,17,2,11,830617,16,840,562,2,2,13,26,5,578,44,6,3,6,11,14,23,666,311,1,5,91,113,48,5,2,1,1,269,355,3,338,168,1,580744,866,256,34,207,1,141,332,6,317,6,58,10,13,9,1,6,8,3,141,112,74,65,35,432,479,1,7,4,187,25,64,146,60050,770,14,563,661,51,777,1,37,561653,168111,29,322,8,36,5,7,634,7,382,2,272,257,129,1,2,9,934,72,25,666,522,406,208,348,135,1,3,1,99,61,45,345,1,1,489,60,65,832,28,151,37,804,68,386,22,122,1,14,1,91,25,27,90,1,290,23,10,11,2,94,53,442,33,157,8,63,11,57,302,813,149,185847,14,208,119,28,533656,112,57,268330,33,5,28,4,17,970,283,38,3,1,564,3,9,117,1,5,522,252,23,2,4,292,20,4,3,231,88,214,45,138,128,192,878,2,290,1,28,10,201,604,1,19,3,378,3,1,591,13,61,2,23,142,6,9,122,478,81,11,858,12,874,15,85454,116,23,635,88,4,930,194,231,2,2,5,1,6,3,3,357,263,115,29,7,14,16,48,205,5,30,1,3,241,217,270,69,295,144,15,15,20,7,1,4,11,1,7,123,5,4,54,1,16,63,6,3,15,963,74,111,2,471,1,644,88,532,11,1,36,47,877,14,4,17,1,352,1,146,33,396,3,14,5,197,2,852,2,602,34,1,34,69,28,383,225,177,2,1,246,2,2,203,15,932,496,154,285,3,10,204,11,4,798088,104,1,6,15,12,324,20,387,871,163,206,67,72,17,1,88,3,3,69,2,3,2,13,5,945,28,361,223,85,3,3,3,7,36,35,161,8,135,126,243,4,11744,3,523,587,990,16,183,4,208,5,2,259,779,4,116,70,388,6,1,37,26,12,1,28,32,8,198,24,38,25,412,2,3,853,27,5,247,3,756,52,579,157,59,22,58,493,12,31,108,52,20,22,47,7,173,12,2,62,2,6,160,4,301,4,1,11,30,2,25,309183,1,97,20,1,5,326,4,6,77,9,212,182,544,112,1,28,64,7,8,364,3,145,95,99,1,63,16,92,112,908,339,54,631,148,963,96,2}

Returns: 6589889
167

392

{57,115,91,147,4,108,73,158,34,76,84,99,150,147,70,156,154,63,101,1,30,67,144,77,76,163,150,143,109,104,166,56,65,46,128,130,21,97,4,71,122,47,2,157,89,14,50,12,111,139,107,66,133,61,109,3,103,32,20,24,145,53,1,2,166,33,155,36,63,4,24,16,155,22,28,138,157,64,47,97,95,136,42,90,3,70,7,158,166,152,162,165,63,23,82,50,51,12,116,155,11,66,110,25,61,116,96,142,87,86,130,120,82,16,105,103,9,11,105,8,101,166,21,145,165,72,94,48,11,153,1,94,134,109,49,94,137,90,0,100,51,65,163,161,86,141,68,71,95,45,148,79,29,73,6,48,137,4,103,26,37,41,159,80,69,124,164,72,144,146,82,52,151,20,138,72,122,49,84,31,146,23,11,84,28,141,166,44,4,143,129,108,37,45,21,93,80,134,142,67,67,0,31,131,99,143,136,122,141,76,135,6,157,9,165,41,73,49,46,140,87,138,75,64,60,58,130,22,71,30,88,44,72,37,107,162,143,56,86,156,139,140,106,23,56,138,5,19,0,127,66,129,32,13,34,1,68,137,154,102,55,26,15,93,125,53,147,75,140,21,119,15,162,123,161,25,37,118,146,118,161,98,107,75,109,12,25,51,84,79,118,76,42,109,48,120,83,140,135,96,141,151,163,131,14,118,23,69,123,106,12,165,102,72,153,54,142,147,125,85,60,135,39,78,126,156,123,104,19,59,159,55,103,128,24,134,115,111,9,31,161,98,36,28,34,73,93,54,98,3,71,151,160,20,53,105,5,131,103,41,37,116,30,97,41,143,148,75,113,31,33,43,15,17,3,100,81,96,163,133,124,123,54,92,19,81,110,95,127,45,82,32,110,6,64,156,26,160,56,74,62,89,78,9,119,43,24,36,138,66,62,32,65,160,88,19,38,124,115,159,6,27,129,130,89,62,59,85,17,113,65,78,136,58,98,107,123,56,139,53,54,117,89,114,106,18,57,155,97,120,67,38,139,133,117,144,90,145,25,57,111,46,121,129,157,30,78,98,43,20,28,40,122,59,108,109,61,146,0,102,106,98,133,59,165,53,134,73,27,158,81,153,44,22,142,119,84,85,5,150,61,2,3,7,111,87,163,149,92,1,127,121,69,38,125,65,77,77,58,90,150,47,70,135,30,88,85,47,34,127,126,10,40,78,162,7,104,47,139,126,104,8,31,133,146,5,115,139,41,48,12,72,121,27,94,144,63,17,27,152,50,6,122,111,1,14,29,159,86,88,132,124,78,150,70,121,85,69,8,59,74,111,96,16,11,154,91,131,10,110,118,140,106,67,58,93,87,117,148,82,114,47,100,55,95,82,134,105,130,128,89,17,149,150,119,104,29,131,49,43,7,2,39,58,92,124,18,31,4,121,26,44,92,55,126,160,108,58,118,76,24,164,62,129,104,18,107,112,146,75,117,63,48,128,161,142,164,81,55,15,135,64,102,0,86,105,20,74,87,45,43,147,13,99,6,153,129,140,46,35,68,101,154,128,95,154,28,40,77,36,100,9,35,12,153,57,10,13,23,113,34,34,83,17,119,39,132,40,35,96,50,154,26,90,136,155,105,16,10,141,74,42,29,55,164,68,83,160,138,85,0,80,74,127,32,120,107,115,53,81,43,93,80,91,51,158,152,52,74,132,60,67,101,11,156,149,83,49,163,54,157,144,8,26,52,117,40,48,110,77,46,41,114,49,116,119,75,39,108,22,42,16,15,153,164,103,56,120,123,30,141,24,52,38,25,14,10,137,106,57,115,102,7,124,44,155,22,158,125,152,36,131,61,145,14,23,83,144,113,33,113,19,8,91,91,64,128,71,79,17,92,68,151,66,37,60,136,148,164,13,159,90,2,35,151,27,42,18,162,66,151,79,33,83,133,60,15,158,94,114,136,112,112,117,39,20,148,77,110,5,100,92,157,101,51,84,116,54,135,38,99,112,79,21,132,9,42,45,50,39,97,93,38,108,22,2,64,19,159,130,121,36,143,152,62,14,91,59,33,132,100,60,68,51,88,29,114,63,65,70,80,10,46,102,97,99,61,120,50,134,113,27,80,62,32,44,25,81,57,116,122,145,127,126,165,114,149,112,52,145,94,147,87,18,33,8,3,125,149,86,96,28,137,29,76,69,148,45,126,95,18,112,137,89,13,7,88,13,69,156,40,52,70,160,79,149,162,152,5,21,142,125,35,132,73,35,71,101,161,99}

{38,157,38,47,134,101,93,30,153,44,131,89,80,109,5,106,42,127,119,124,152,96,3,71,134,149,164,130,145,43,74,48,28,77,34,166,32,63,128,126,80,22,48,36,19,34,79,158,62,19,107,80,133,65,27,92,108,132,131,24,87,60,61,165,143,51,162,64,0,127,77,29,42,77,36,31,144,163,121,26,156,144,126,43,29,47,156,20,34,154,141,154,153,67,166,73,55,63,137,116,136,148,162,86,33,135,96,140,38,37,17,140,61,4,42,2,121,132,75,32,134,81,2,36,12,28,87,26,44,154,143,33,12,51,47,70,29,119,75,76,72,23,9,54,5,119,40,72,123,143,20,27,104,142,164,134,145,159,64,11,40,109,10,2,97,27,109,134,53,13,107,108,29,140,11,46,146,164,137,48,128,3,144,60,27,102,79,76,137,54,49,133,21,55,52,10,134,88,13,89,14,116,138,128,17,38,133,148,71,8,68,111,88,151,66,32,9,104,119,96,141,126,137,92,150,32,49,17,92,166,161,4,90,52,77,21,113,38,3,121,109,1,51,108,114,95,12,122,11,107,27,80,148,134,106,3,80,83,117,97,97,129,46,129,110,126,7,134,119,52,81,103,27,89,7,78,49,6,38,22,100,89,21,140,144,74,49,113,122,80,55,27,93,55,17,110,18,155,114,28,63,164,12,135,22,68,72,40,134,37,31,10,117,15,69,129,113,56,37,165,79,2,128,150,0,79,2,111,54,68,72,15,17,164,41,127,68,83,145,66,13,96,130,25,117,45,25,17,69,56,127,17,98,142,72,9,103,66,133,50,124,145,81,76,16,123,87,122,126,156,80,1,59,130,111,115,160,25,65,131,81,116,3,39,157,35,166,90,78,88,6,80,150,22,5,55,67,142,67,30,63,150,42,51,158,36,90,15,112,22,124,57,7,106,143,68,108,149,165,79,147,55,90,30,150,164,101,142,0,75,22,9,66,80,124,93,78,34,95,49,37,59,102,62,153,84,157,46,65,53,77,59,34,137,166,119,163,102,112,84,11,79,162,117,29,102,24,83,32,92,7,136,30,67,21,135,63,2,110,131,91,63,136,142,44,122,11,134,65,55,70,159,26,117,93,122,114,152,112,117,48,40,16,118,123,166,157,24,106,157,114,112,137,80,93,108,65,112,26,162,137,134,96,49,59,82,70,0,89,71,132,144,88,157,109,143,43,98,41,110,1,158,153,88,74,130,115,132,81,22,148,93,17,82,81,123,164,92,31,30,45,159,76,153,17,121,28,141,64,74,120,33,31,10,143,26,109,15,59,41,12,117,39,158,136,2,50,133,139,76,132,87,75,36,17,123,112,42,104,2,164,87,166,117,162,116,100,60,106,52,163,76,69,111,151,144,79,132,152,22,52,156,27,20,12,8,137,16,52,123,89,122,37,131,137,122,35,161,124,43,80,47,119,133,39,52,24,57,3,104,44,60,17,69,50,111,164,92,71,152,57,79,70,114,140,26,52,30,51,124,13,125,31,80,114,129,69,115,75,134,9,100,85,153,131,119,16,68,72,135,19,159,111,151,107,138,99,15,76,141,1,116,161,86,127,18,98,97,1,106,23,122,2,6,142,124,110,14,41,58,32,95,156,7,137,137,84,100,38,118,5,126,80,16,53,18,147,0,6,134,33,141,76,82,23,104,92,28,53,82,95,131,86,111,139,73,117,59,59,135,21,11,101,96,76,139,51,114,103,23,79,40,86,126,82,35,72,125,5,140,118,158,138,151,98,164,74,105,58,139,63,107,20,96,92,92,1,151,131,115,97,86,28,14,30,33,148,49,19,38,83,97,118,101,13,125,79,16,85,110,26,85,144,144,70,134,81,89,9,31,141,154,25,62,66,120,98,56,27,46,47,8,98,73,81,146,88,11,150,147,54,12,55,73,166,62,128,106,156,116,37,140,139,20,155,9,106,153,87,87,165,166,133,152,116,166,56,124,37,96,106,166,39,152,157,111,101,33,96,117,128,141,131,105,76,114,135,101,13,53,44,91,101,27,156,111,165,104,11,39,43,87,57,64,102,107,75,123,103,88,143,102,5,15,153,89,74,50,163,39,30,61,27,54,103,162,18,164,1,0,70,110,154,133,83,38,89,16,82,60,74,63,102,108,108,69,57,7,138,76,18,123,28,157,69,143,8,121,130,62,102,60,115,55,77,64,63,130,82,145,147,69,152,92,124,133,107,29,89,42,39,52,31,2,15,45,137,27,66,72}

{61,1,50,531,189,865,2,33,164,1,8,64,1,102,2,24,574,6,569,340,6,1,171,553,13,19,680,687,673,2,234,76,13,31,72,29,382,367,698,48,19,362,122,26,935,58,4,12,305,1,4,699,138,3,31,10,27,1,72,64,647,342,2,76,122,77,82,2,306,150,6,1,83,3,121,59,121,1,87,37,287,50,3,67,678,6,39,3,2,97,19,357,882,1,36,63,1,24,17,60,12,36,1,495,413,232,6,4,1,41,60,13,2,22,18,107,1,133,3,857,27,11,4,5,62,6,23,95,143,804,497,5,1,788,366,1,27,285,9,1,21,228,209,1,5,110,291,3,133,3,1,2,295,60,374,11,215,20,4,26,19,171,49,77,6,112,919,2,3,149,11,590,12,31,2,1,894,7,76,122,602,100,2,3,468,860,21,2,11,14,11,402,3,22,646,3,7,581,1,1,69,456,3,52,33,1,1,88,1,62,9,668,8,150,15,74,21,371,171,243,124,14,749,831,908,87,48,8,356,36,3,238,8,9,5,13,615,37,17,6,1,3,5,552,1,186,12,1,40,21,806,2,17,360,5,236,448,387,1,66,82,94,1,115,39,1,13,5,1,9,4,1,1,3,1,2,9,1,30,779,7,1,1,998,165,17,35,11,68,46,47,848,1,2,231,2,12,1,1,16,37,308,410,8,2,56,11,11,922,191,53,27,873,844,58,14,3,4,23,47,12,10,718,1,979,6,576,30,8,37,6,17,32,71,906,2,1,135,10,140,59,175,17,7,1,1,276,30,11,51,127,412,2,33,140,5,16,506,188,9,4,2,102,28,88,2,17,54,27,1,122,13,46,1,2,33,25,3,490,902,709,572,32,1,22,178,3,50,583,51,1,17,147,289,105,22,199,554,2,146,2,16,805,190,141,1,2,1,421,357,462,11,54,1,438,4,413,206,32,23,4,20,119,14,1,22,181,186,1,306,2,41,99,586,464,1,68,17,46,5,118,3,26,1,2,175,707,4,3,2,9,5,1,1,1,13,24,4,57,25,621,284,123,41,95,5,40,3,62,17,8,218,21,6,1,38,20,448,568,1,1,283,97,16,402,796817,27,409,10,36,2,79,38,23,24,161,1,489,138,1,620,127,8,271,23,23,17,295,85,25,32,504,4,2,43,2,4,4,103,41,145,3,113,1,2,2,2,470,306,4,1,31,8,920713,2,46,499,5,88,44,180,68,8,90,2,23,9,245,10,2,830,86,4,241,372,55,11,178,5,251,578,11,14,178,7,428,634,128,8,1,92,7,286,1,283,6,53,3,7,3,145,20,45,305,6,275,61,75,3,1,1,33,98,3,686,54,269,2,25,367,3,1,51,102,924,607,13,3,37,5,8,2,376,80,9,28,2,1,255,1,12,359,108,148,357,1,301,1,4,869,9,80,913,67,276,72,1,69,1,3,17,3,13,82,21,984,46,31,51,11,591,258,1,41,996,76,111,230,46,86,6,1,1,39,223,698,32,4,711,29,353,8,18,487,159,786,70,4,313,169,4,15,727,334,123,1,126,1,123,82,1,29,683,309,3,9,411,2,173,522,3,37,567915,7,46,24,1,291,1,362,4,17,256,171,8,12,568,114,59,2,640,90,8,685,84,46,808,8,33,21,16,145,71,9,227,5,153,83,885,4,26,11,785,112,476,17,827,3,185,3,488,1,1,247,34,57,320,474,1,20,5,393,1,12,45,4,24,98,1,1,2,608,1,1,118,159,5,26,4,39,1,8,23,7,11,301,155,4,350,14,392,3,6,36,38,20,1,559,59,3,216,133,221,459,2,35,38,1,5,155,340,16,346,16,1,798212,1,269,657,19,178,20,2,4,2,198,8,9,1,134,132,50,1,186,997,2,2,32,27,2,4,11,118,3,443,12,29,20,17,23,11,24,1,6,2,69,124,120,170,1,22,15,22,27,3,31,13,1,12,27,13,303,118,72,168,31,822,17,658,2,3,328,283,278,96,98,3,1,1,140,28,4,867,4,1,2,194,2,3,58,743,779,976,778,137,5,18,6,14,10,120,63,66,300,69,30,9,1,203,562,39,6,283,2,7,3,24,257,873,37,301,3,312,1,42,12,64,977,34,30,112,494,2,428,128,14,87,820,5,785,6,12,129,912,23,5,14,146,4,7,13,295,28,2,4,42,342,54,57,36,397169,1,6,8,31,17,71,15,2,719,9,811,3,14,169,98,16,426,16,909,740,1,6,22,34,191,699,1,154,3}

Returns: 90132243
7

1

{0,0,1,1,1,2,2,3,3,4,4,5,5,6,6}

{0,1,2,5,6,0,4,0,4,3,4,5,0,6,6}

{0,10,1,2,8,10,0,10000,0,0,10,0,100,22,33}

Returns: 130
351

272

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Returns: 253741196
467

963

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Returns: 1786164476
50

200

{0, 13, 8, 17, 3, 8, 4, 21, 11, 20, 2, 18, 21, 2, 4, 9, 17, 0, 14, 10, 15, 18, 1, 22, 10, 14, 19, 24, 5, 5, 12, 7, 7, 16, 19, 13, 20, 15, 23, 6, 23, 9, 3, 6, 16, 11, 22, 24, 12, 1, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 37, 9, 14, 0, 33, 20, 46, 26, 12, 11, 2, 7, 34, 19, 37, 5, 2, 17, 41, 16, 34, 13, 18, 35, 6, 14, 16, 25, 9, 10, 5, 10, 7, 36, 45, 3, 6, 22, 32, 28, 45, 40, 16, 36, 28, 16, 34, 1, 9, 19, 18, 6, 15, 29, 12, 5, 44, 33, 49, 14, 40, 1, 30, 21, 37, 49, 1, 44, 42, 6, 38, 1, 31, 40, 37, 34, 35, 6, 43, 29, 41, 48, 17, 4, 38, 26, 4, 46, 43, 6, 27, 30, 0, 16, 40, 33, 0, 42, 41, 10, 33, 47, 11, 37, 49, 25, 36, 20, 47, 12, 28, 17, 11, 17, 26, 26, 37, 34, 27, 17, 8, 2, 13, 43, 36, 28, 1, 23, 29, 40, 18, 22, 0, 7, 30, 23, 3, 39, 5, 23, 28, 38, 44, 19, 43, 15, 16, 43, 5, 27, 24, 25, 7, 16, 38, 33, 33, 1, 9, 25, 47, 0, 31, 30, 29, 4, 36, 49, 26, 6, 39, 40, 28, 39, 48, 26, 2, 15, 41, 42, 32, 0, 35, 34, 28, 30, 40, 3, 33, 16, 15, 41, 45, 12, 33, 35, 16, 47, 34, 23 }

{41, 42, 17, 0, 2, 7, 28, 32, 31, 33, 6, 42, 11, 13, 7, 40, 47, 21, 4, 6, 19, 15, 4, 18, 30, 25, 2, 10, 30, 34, 1, 47, 35, 23, 3, 0, 9, 25, 42, 21, 4, 6, 47, 32, 5, 40, 5, 0, 8, 49, 16, 29, 8, 11, 42, 33, 35, 26, 27, 43, 35, 6, 14, 13, 44, 25, 13, 42, 2, 26, 17, 3, 40, 31, 18, 12, 24, 37, 0, 37, 15, 44, 35, 40, 10, 1, 35, 47, 36, 33, 2, 39, 23, 28, 32, 0, 6, 21, 33, 41, 0, 19, 16, 29, 35, 16, 44, 6, 18, 17, 2, 46, 41, 11, 27, 5, 44, 1, 48, 15, 43, 8, 41, 33, 16, 11, 45, 47, 19, 41, 14, 41, 8, 24, 13, 3, 44, 41, 42, 30, 31, 44, 21, 14, 43, 48, 0, 6, 25, 38, 36, 14, 36, 22, 43, 15, 20, 19, 37, 25, 17, 44, 17, 46, 8, 25, 33, 19, 42, 40, 42, 24, 15, 31, 34, 8, 41, 25, 20, 29, 2, 5, 43, 28, 33, 40, 31, 27, 6, 21, 9, 35, 8, 8, 26, 13, 11, 31, 4, 4, 30, 34, 35, 1, 15, 11, 10, 24, 15, 24, 23, 16, 24, 32, 9, 1, 6, 17, 48, 6, 35, 19, 12, 5, 21, 23, 25, 9, 17, 47, 19, 23, 22, 35, 19, 5, 1, 10, 9, 41, 11, 45, 0, 23, 0, 11, 39, 0, 17, 2, 18, 4, 17, 24, 0, 10, 19, 4, 36, 22, 42, 18, 13, 48, 27, 11, 19, 28, 31, 39, 32, 48, 2, 26, 38, 43, 38, 49, 34, 37, 11, 9, 11, 14, 12, 9, 37, 0, 22, 14, 15, 0, 8, 23, 7, 43, 5, 8, 16, 47 }

{494, 848305, 3326, 6008, 223, 2, 6, 673, 152335, 25, 713909, 42842, 122, 9941, 361853, 35, 20157, 1098, 41, 83693, 365851, 43843, 622, 591230, 7722, 2489, 7, 861622, 21272, 169, 1153, 3, 7, 3, 577031, 24522, 5, 241, 757900, 11036, 8892, 199, 7, 2, 1, 453031, 115, 13, 125, 67, 35, 91, 33427, 14, 106, 203749, 5, 1804, 4543, 23, 1, 281, 441212, 18, 3, 11629, 233, 388188, 10, 701, 76170, 763, 875, 11606, 44972, 6449, 37409, 83516, 5912, 6, 705899, 26759, 253, 580531, 14215, 21916, 884775, 30, 678, 5940, 17, 480830, 8, 61, 218613, 683352, 4, 557589, 2619, 3658, 221515, 15825, 163577, 25, 9, 1, 4, 13, 2, 88, 147, 110163, 18118, 2, 15429, 211872, 24, 1, 188382, 12500, 2348, 190, 4279, 40, 8428, 56325, 933152, 231523, 9454, 21, 4855, 96168, 1722, 329515, 77, 1, 3, 3518, 10926, 12172, 4, 71, 181976, 1318, 9, 5086, 905, 108490, 80164, 2, 10236, 197, 1880, 17420, 614650, 372457, 13918, 36, 17, 167, 6, 254127, 512, 15, 341436, 1, 186, 96, 7, 3, 42, 4, 3, 4, 492598, 18523, 172302, 1, 421535, 390382, 2952, 6228, 871, 505372, 131266, 5, 743902, 11, 34, 657, 4717, 3196, 259, 192504, 229, 6786, 28, 44364, 21123, 8, 166781, 885021, 2, 828, 497, 376, 24707, 52, 1, 1659, 19402, 27261, 82, 473, 443, 1089, 586, 20, 7, 239277, 27132, 4681, 761, 10644, 17798, 1, 820306, 13330, 19, 293167, 2, 4, 89279, 14, 1, 9, 18023, 1165, 495221, 32304, 538, 178613, 1, 4764, 32767, 114, 103, 1, 302, 428, 92, 927352, 22270, 2646, 3599, 6, 16362, 3, 4, 280286, 338, 652, 2, 347022, 23, 323084, 3338, 46, 58, 1263, 93, 46992, 19112, 1, 19499, 33, 807600, 20296, 16803, 911294, 3151, 1, 793, 1, 1, 504, 62209, 1397, 52726, 3650, 54, 3630, 358480, 178, 394, 28, 137436, 52764, 1209, 1599 }

Returns: 121213509
3

1000

{0, 1, 1, 2 }

{1, 0, 2, 2 }

{3, 2, 1, 1 }

Returns: 5004
50

1000

{0, 13, 8, 17, 3, 8, 4, 21, 11, 20, 2, 18, 21, 2, 4, 9, 17, 0, 14, 10, 15, 18, 1, 22, 10, 14, 19, 24, 5, 5, 12, 7, 7, 16, 19, 13, 20, 15, 23, 6, 23, 9, 3, 6, 16, 11, 22, 24, 12, 1, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 37, 9, 14, 0, 33, 20, 46, 26, 12, 11, 2, 7, 34, 19, 37, 5, 2, 17, 41, 16, 34, 13, 18, 35, 6, 14, 16, 25, 9, 10, 5, 10, 7, 36, 45, 3, 6, 22, 32, 28, 45, 40, 16, 36, 28, 16, 34, 1, 9, 19, 18, 6, 15, 29, 12, 5, 44, 33, 49, 14, 40, 1, 30, 21, 37, 49, 1, 44, 42, 6, 38, 1, 31, 40, 37, 34, 35, 6, 43, 29, 41, 48, 17, 4, 38, 26, 4, 46, 43, 6, 27, 30, 0, 16, 40, 33, 0, 42, 41, 10, 33, 47, 11, 37, 49, 25, 36, 20, 47, 12, 28, 17, 11, 17, 26, 26, 37, 34, 27, 17, 8, 2, 13, 43, 36, 28, 1, 23, 29, 40, 18, 22, 0, 7, 30, 23, 3, 39, 5, 23, 28, 38, 44, 19, 43, 15, 16, 43, 5, 27, 24, 25, 7, 16, 38, 33, 33, 1, 9, 25, 47, 0, 31, 30, 29, 4, 36, 49, 26, 6, 39, 40, 28, 39, 48, 26, 2, 15, 41, 42, 32, 0, 35, 34, 28, 30, 40, 3, 33, 16, 15, 41, 45, 12, 33, 35, 16, 47, 34, 23 }

{41, 42, 17, 0, 2, 7, 28, 32, 31, 33, 6, 42, 11, 13, 7, 40, 47, 21, 4, 6, 19, 15, 4, 18, 30, 25, 2, 10, 30, 34, 1, 47, 35, 23, 3, 0, 9, 25, 42, 21, 4, 6, 47, 32, 5, 40, 5, 0, 8, 49, 16, 29, 8, 11, 42, 33, 35, 26, 27, 43, 35, 6, 14, 13, 44, 25, 13, 42, 2, 26, 17, 3, 40, 31, 18, 12, 24, 37, 0, 37, 15, 44, 35, 40, 10, 1, 35, 47, 36, 33, 2, 39, 23, 28, 32, 0, 6, 21, 33, 41, 0, 19, 16, 29, 35, 16, 44, 6, 18, 17, 2, 46, 41, 11, 27, 5, 44, 1, 48, 15, 43, 8, 41, 33, 16, 11, 45, 47, 19, 41, 14, 41, 8, 24, 13, 3, 44, 41, 42, 30, 31, 44, 21, 14, 43, 48, 0, 6, 25, 38, 36, 14, 36, 22, 43, 15, 20, 19, 37, 25, 17, 44, 17, 46, 8, 25, 33, 19, 42, 40, 42, 24, 15, 31, 34, 8, 41, 25, 20, 29, 2, 5, 43, 28, 33, 40, 31, 27, 6, 21, 9, 35, 8, 8, 26, 13, 11, 31, 4, 4, 30, 34, 35, 1, 15, 11, 10, 24, 15, 24, 23, 16, 24, 32, 9, 1, 6, 17, 48, 6, 35, 19, 12, 5, 21, 23, 25, 9, 17, 47, 19, 23, 22, 35, 19, 5, 1, 10, 9, 41, 11, 45, 0, 23, 0, 11, 39, 0, 17, 2, 18, 4, 17, 24, 0, 10, 19, 4, 36, 22, 42, 18, 13, 48, 27, 11, 19, 28, 31, 39, 32, 48, 2, 26, 38, 43, 38, 49, 34, 37, 11, 9, 11, 14, 12, 9, 37, 0, 22, 14, 15, 0, 8, 23, 7, 43, 5, 8, 16, 47 }

{494, 848305, 3326, 6008, 223, 2, 6, 673, 152335, 25, 713909, 42842, 122, 9941, 361853, 35, 20157, 1098, 41, 83693, 365851, 43843, 622, 591230, 7722, 2489, 7, 861622, 21272, 169, 1153, 3, 7, 3, 577031, 24522, 5, 241, 757900, 11036, 8892, 199, 7, 2, 1, 453031, 115, 13, 125, 67, 35, 91, 33427, 14, 106, 203749, 5, 1804, 4543, 23, 1, 281, 441212, 18, 3, 11629, 233, 388188, 10, 701, 76170, 763, 875, 11606, 44972, 6449, 37409, 83516, 5912, 6, 705899, 26759, 253, 580531, 14215, 21916, 884775, 30, 678, 5940, 17, 480830, 8, 61, 218613, 683352, 4, 557589, 2619, 3658, 221515, 15825, 163577, 25, 9, 1, 4, 13, 2, 88, 147, 110163, 18118, 2, 15429, 211872, 24, 1, 188382, 12500, 2348, 190, 4279, 40, 8428, 56325, 933152, 231523, 9454, 21, 4855, 96168, 1722, 329515, 77, 1, 3, 3518, 10926, 12172, 4, 71, 181976, 1318, 9, 5086, 905, 108490, 80164, 2, 10236, 197, 1880, 17420, 614650, 372457, 13918, 36, 17, 167, 6, 254127, 512, 15, 341436, 1, 186, 96, 7, 3, 42, 4, 3, 4, 492598, 18523, 172302, 1, 421535, 390382, 2952, 6228, 871, 505372, 131266, 5, 743902, 11, 34, 657, 4717, 3196, 259, 192504, 229, 6786, 28, 44364, 21123, 8, 166781, 885021, 2, 828, 497, 376, 24707, 52, 1, 1659, 19402, 27261, 82, 473, 443, 1089, 586, 20, 7, 239277, 27132, 4681, 761, 10644, 17798, 1, 820306, 13330, 19, 293167, 2, 4, 89279, 14, 1, 9, 18023, 1165, 495221, 32304, 538, 178613, 1, 4764, 32767, 114, 103, 1, 302, 428, 92, 927352, 22270, 2646, 3599, 6, 16362, 3, 4, 280286, 338, 652, 2, 347022, 23, 323084, 3338, 46, 58, 1263, 93, 46992, 19112, 1, 19499, 33, 807600, 20296, 16803, 911294, 3151, 1, 793, 1, 1, 504, 62209, 1397, 52726, 3650, 54, 3630, 358480, 178, 394, 28, 137436, 52764, 1209, 1599 }

Returns: 607281928
3

1000

{0, 1, 2 }

{1, 0, 0 }

{1000000, 1000000, 1000000 }

Returns: -1
3

100

{0, 0, 2, 1 }

{1, 2, 2, 1 }

{1, 1, 1, 1 }

Returns: -1
1000

1000

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 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Returns: 99999900000

Statistics

Problem Statement for "MaliciousPath"

Problem Statement

Definition

Constraints

Examples