Statistics

Problem Statement for "CRTFun"

Problem Statement

You will be given a int[] mods such that no two distinct elements of mods share a factor greater than 1. In other words, every pair of distinct elements will be relatively prime. Let P denote the product of the integers in mods. Someone has picked an integer between 0 and P-1 inclusive, but they won't tell you it. Instead they reveal what the number is mod k, for each k in mods. The ith element of vals will be the value of the picked number mod the ith element of mods. For example, if 
	mods = { 2, 3, 5, 7 }, and 
	vals = { 1, 2, 2, 5 },
then the number in question will satisfy the following congruences: 
	number mod 2 = 1 ,
	number mod 3 = 2 ,
	number mod 5 = 2 , and
	number mod 7 = 5 .
Return the picked number. To simplify matters, the picked number will never be greater than 100000.

Definition

Class:
CRTFun
Method:
findSolution
Parameters:
int[], int[]
Returns:
int
Method signature:
int findSolution(int[] mods, int[] vals)
(be sure your method is public)

Notes

  • The solution will always be unique.

Constraints

  • mods will contain between 2 and 50 elements inclusive.
  • Each element of mods will be between 2 and 100000 inclusive.
  • Each element of mods will be distinct.
  • No two distinct elements of mods will share a factor other than 1.
  • vals will contain the same number of elements as mods.
  • vals[i] is between 0 and mods[i]-1 inclusive.
  • The picked number will be between 0 and 100000 inclusive.
  • In addition, the picked number will be less than P, where P is the product of the elements in mods.

Examples

  1. { 2, 3, 5, 7 }

    { 1, 2, 2, 5 }

    Returns: 47

    From above.

  2. { 5, 13 }

    { 2, 3 }

    Returns: 42

  3. { 5 , 11 }

    { 4 , 5 }

    Returns: 49

  4. { 9, 8, 7 }

    { 1, 2, 3 }

    Returns: 10

  5. { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}

    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    Returns: 0

  6. { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}

    { 0, 0, 2, 5, 1, 9, 11, 10, 5, 17, 18, 34}

    Returns: 99342

  7. {343,1331,2197,4913,6859,12167,24389,29791,50653,68921,79507}

    {221,1026,945,3903,3999,1793,13905,8503,38294,38294,38294}

    Returns: 38294

  8. {2,3}

    {0,0}

    Returns: 0

  9. {2,3}

    {1,2}

    Returns: 5

  10. {6018,65257,31129,91117,54797,86011,14285,81899,49373,83137,91211,1633,40529,90133,6551,23819,45841,32027,99109,7279,39497,21577,11171,26711,68863,87053,4243,41669,81943,30319,98071,2563,65027,75217,90011,53741,67549,69709,2003,7549,71647,43583,52963,58787,56779,52951,36709,76873,77167,36529}

    {3198,16175,19174,81432,26635,81432,10007,81432,32059,81432,81432,1415,374,81432,2820,9975,35591,17378,81432,1363,2438,16701,3235,1299,12569,81432,815,39763,81432,20794,81432,1979,16405,6215,81432,27691,13883,11723,1312,5942,9785,37849,28469,22645,24653,28481,8014,4559,4265,8374}

    Returns: 81432

  11. {29023,15971,68433,82286,34319,50291,57511,54853,80945,58681,79721,88393,79739,31751,61459,35729,82993,45217,38149,16469,25559,2897,7297,30491,87253,48613,18049,62233,98639,16433,75983,92261,70201,8627,98017,70489,65861,96179,17089,8707,93083,35671,269,66569,29021,46681,85333,44857,99787,18503}

    {24045,5155,53068,53068,18749,2777,53068,53068,53068,53068,53068,53068,53068,21317,53068,17339,53068,7851,14919,3661,1950,922,1989,22577,53068,4455,16970,53068,53068,3769,53068,53068,53068,1306,53068,53068,53068,53068,1801,826,53068,17397,75,53068,24047,6387,53068,8211,53068,16062}

    Returns: 53068

  12. {62845,89354,64711,81879,23137,38671,48089,26171,6761,96871,66797,67157,17209,67049,36637,88913,61321,80317,54259,7409,47273,99299,49927,63641,54097,2083,35369,16139,34319,27437,68599,59377,35527,8089,14129,86857,98027,63299,13711,23557,12511,78803,54193,13757,38501,86263,83077,25037,91691,50539}

    {11323,11323,11323,11323,11323,11323,11323,11323,4562,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,3914,11323,11323,11323,11323,11323,908,11323,11323,11323,11323,11323,11323,11323,3234,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323,11323}

    Returns: 11323

  13. {98130,21073,20599,95393,18257,13661,40099,31139,42091,54689,56387,70307,39343,26419,77437,10901,76243,56123,11069,81559,4831,1297,18833,3163,56131,94019,7297,43867,38239,28991,11677,77461,20557,45061,99487,57089,74267,7781,40867,21817,19609,46471,52291,99401,93949,38167,80219,19781,61681,41969}

    {57572,15426,16374,57572,2801,2928,17473,26433,15481,2883,1185,57572,18229,4734,57572,3067,57572,1449,2227,57572,4431,504,1073,638,1441,57572,6493,13705,19333,28581,10864,57572,16458,12511,57572,483,57572,3105,16705,13938,18354,11101,5281,57572,57572,19405,57572,18010,57572,15603}

    Returns: 57572

  14. {62425,19957,98396,71259,80657,72349,33623,51547,40963,99529,42967,70673,83393,90619,15473,87811,37561,86077,6211,96983,98489,63619,13691,93661,41647,93949,45767,51299,35297,23801,36581,6977,74189,76859,36109,78593,83533,83977,10771,2993,89189,5569,34231,16223,32359,57143,25447,83323,75007,73037}

    {3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488,495,3488,3488,3488,3488,3488,3488,3488,3488,3488,3488}

    Returns: 3488

  15. {69530,11291,32201,31363,72559,66943,9679,74731,78177,76243,94103,44911,1123,2267,99499,31643,10561,27509,98071,29173,1327,58153,65413,77711,4427,55339,56999,87781,56299,91297,27763,88147,40259,44677,59779,5167,50423,46747,52523,90499,80147,38921,75367,98563,10061,93559,11447,71443,82349,27239}

    {13508,4001,18636,20312,10479,16095,5606,8307,4861,6795,83038,38127,1059,1426,83038,19752,9111,511,83038,24692,764,24885,17625,5327,3352,27699,26039,83038,26739,83038,27512,83038,2520,38361,23259,366,32615,36291,30515,83038,2891,5196,7671,83038,2550,83038,2909,11595,689,1321}

    Returns: 83038

  16. {34815,56461,99874,29879,79301,65069,16319,16501,60341,48181,55381,99391,25901,35393,69119,76961,10891,55981,86057,21047,56809,97303,19961,55417,60607,16879,35359,76411,37747,49771,52523,23971,14327,84499,39911,46103,65251,75109,56743,38219,65393,12931,52627,39133,45641,24919,47239,73063,91753,34739}

    {25915,25915,25915,25915,25915,25915,9596,9414,25915,25915,25915,25915,14,25915,25915,25915,4133,25915,25915,4868,25915,25915,5954,25915,25915,9036,25915,25915,25915,25915,25915,1944,11588,25915,25915,25915,25915,25915,25915,25915,25915,53,25915,25915,25915,996,25915,25915,25915,25915}

    Returns: 25915

  17. {2414,6761,99681,13169,32675,63133,49393,72823,31309,91709,28129,30181,55907,69791,79273,59803,78293,20941,75737,40259,68989,58613,23537,15887,90247,10271,25943,74419,91571,64747,72521,29789,18047,67429,57401,51431,33637,47147,76273,51137,90407,61907,59051,81409,50861,91141,36277,91129,34889,17471}

    {2,6754,33798,7460,1123,33798,33798,33798,2489,33798,5669,3617,33798,33798,33798,33798,33798,12857,33798,33798,33798,33798,10261,2024,33798,2985,7855,33798,33798,33798,33798,4009,15751,33798,33798,33798,161,33798,33798,33798,33798,33798,33798,33798,33798,33798,33798,33798,33798,16327}

    Returns: 33798

  18. {73266,20269,39073,1951,96103,16703,14071,43657,43793,52015,38323,86311,6803,1103,68041,67511,58189,96323,90451,54569,37141,60269,83459,1081,28307,383,11057,52189,31627,45557,29749,40483,97523,72551,46427,25523,42089,98383,63377,59369,67577,93053,65869,35227,21529,8861,89123,26687,94331,87517}

    {51234,10696,12161,508,51234,1125,9021,7577,7441,51234,12911,51234,3613,496,51234,51234,51234,51234,51234,51234,14093,51234,51234,427,22927,295,7006,51234,19607,5677,21485,10751,51234,51234,4807,188,9145,51234,51234,51234,51234,51234,51234,16007,8176,6929,51234,24547,51234,51234}

    Returns: 51234

  19. {88216,56755,83959,14451,30151,58601,33097,74071,44911,69031,49099,14441,86381,37889,9923,68479,97219,84467,15889,13091,64313,19583,32993,40577,4447,54413,71293,93559,21361,44987,21293,85093,66029,59989,76243,3271,39971,32803,76499,81203,64567,26759,99413,3389,35683,73981,48221,5381,74023,56807}

    {61091,4336,61091,3287,789,2490,27994,61091,16180,61091,11992,3327,61091,23202,1553,61091,61091,61091,13424,8727,61091,2342,28098,20514,3280,6678,61091,61091,18369,16104,18505,61091,61091,1102,61091,2213,21120,28288,61091,61091,61091,7573,61091,89,25408,61091,12870,1900,61091,4284}

    Returns: 61091

  20. {37329,98306,5917,72701,90373,27371,10687,87677,33253,96365,12983,93809,39713,92029,44609,2087,72203,53927,5441,23671,75001,11593,39757,23797,42437,59123,35579,49993,8777,84299,46933,13723,91493,64489,68657,29587,59573,67141,96199,71999,7939,653,39821,25073,94903,93941,80911,45319,5413,659}

    {5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,1312,5486,5486,45,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,5486,262,5486,5486,5486,5486,5486,5486,73,214}

    Returns: 5486

  21. {71747,35825,32443,29563,78042,73621,82661,98239,66047,21361,80477,54169,92873,14771,28399,233,82417,37273,86897,77009,35993,72727,68903,38351,62891,13309,17627,48053,17351,73433,74563,68617,74453,51809,97249,80449,77423,30049,61001,93199,71189,86257,75629,73877,94583,83177,3617,11887,42043,91291}

    {44907,9082,12464,15344,44907,44907,44907,44907,44907,2185,44907,44907,44907,594,16508,171,44907,7634,44907,44907,8914,44907,44907,6556,44907,4980,9653,44907,10205,44907,44907,44907,44907,44907,44907,44907,44907,14858,44907,44907,44907,44907,44907,44907,44907,44907,1503,9246,2864,44907}

    Returns: 44907

  22. {2085,11029,70078,68591,143,58777,25457,91567,77983,21199,86297,89303,89087,2039,36863,26711,70111,60449,28993,17713,19429,55331,70957,61517,79061,92527,73973,8741,10687,13721,43601,87877,8693,62371,78007,60589,66823,45119,78307,33821,9613,33871,34169,26783,12227,31307,54013,76667,25633,11681}

    {1324,4559,59704,59704,73,927,8790,59704,59704,17306,59704,59704,59704,573,22841,6282,59704,59704,1718,6565,1417,4373,59704,59704,59704,59704,59704,7258,6269,4820,16103,59704,7546,59704,59704,59704,59704,14585,59704,25883,2026,25833,25535,6138,10796,28397,5691,59704,8438,1299}

    Returns: 59704

  23. {78855,4666,93031,75433,73799,91807,16463,95353,34787,19183,97,39731,24587,30241,28561,24223,70079,46793,30929,22247,42311,1493,48707,64451,76133,52289,24881,55439,98113,65993,54983,3467,32651,66673,5059,96211,69859,73883,59321,9181,71983,1193,91801,65479,82217,79073,36923,97771,44131,8669}

    {25657,2327,25657,25657,25657,25657,9194,25657,25657,6474,49,25657,1070,25657,25657,1434,25657,25657,25657,3410,25657,276,25657,25657,25657,25657,776,25657,25657,25657,25657,1388,25657,25657,362,25657,25657,25657,25657,7295,25657,604,25657,25657,25657,25657,25657,25657,25657,8319}

    Returns: 25657

  24. {6255,55936,49829,68581,39863,38813,45403,7127,25217,89,22837,66739,73037,20507,75799,17413,32891,45979,9887,55723,85021,80273,74027,4001,56891,19079,61729,35083,54433,86803,73633,37171,10853,51071,96127,92593,64093,16873,42577,52993,96179,70181,9839,91591,2113,26339,96713,79301,21737,38653}

    {5111,17980,24087,5335,34053,35103,28513,2646,23482,46,5405,7177,879,12395,73916,4264,8134,27937,4707,18193,73916,73916,73916,1898,17025,16679,12187,3750,19483,73916,283,36745,8798,22845,73916,73916,9823,6424,31339,20923,73916,3735,5043,73916,2074,21238,73916,73916,8705,35263}

    Returns: 73916

  25. {5909,89827,11461,12594,97133,74779,89177,33601,63709,71371,19661,65093,99401,30925,34577,26221,51217,3137,4379,66197,14327,81371,25343,94637,75773,27653,11303,19693,86027,17579,39917,19933,76529,88591,54679,74587,14099,29573,14699,24169,57457,62879,59803,27257,96043,12073,21563,65423,78209,21341}

    {4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,1334,92,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471,4471}

    Returns: 4471

  26. {34149,21196,24323,26687,37525,24013,90751,10609,31789,2179,29863,22679,36853,76541,43117,24331,91787,89027,26743,42937,38641,99013,71419,96359,95519,26567,69019,85469,68909,58943,26869,91771,35111,39379,52837,9619,90353,47743,31153,38407,90379,43457,66041,55577,95239,23339,9041,81853,3671,52579}

    {23164,1968,23164,23164,23164,23164,23164,1946,23164,1374,23164,485,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,3926,23164,23164,23164,23164,23164,23164,23164,23164,23164,23164,5082,23164,1138,23164}

    Returns: 23164

  27. {55605,91822,74837,62221,28921,89693,80021,45491,40169,41311,38483,57997,98369,61319,98723,33301,14747,56503,3373,32353,66587,72911,85499,9409,30941,93209,79693,72553,28549,91811,6767,62749,67663,9209,19381,37837,85081,9157,53891,42907,53527,17117,88027,44483,69403,56137,76487,9109,63751,58013}

    {9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,9986,3240,9986,9986,9986,9986,577,9986,9986,9986,9986,9986,9986,3219,9986,9986,777,9986,9986,9986,829,9986,9986,9986,9986,9986,9986,9986,9986,9986,877,9986,9986}

    Returns: 9986

  28. {1045,68774,44419,18993,59087,31067,78307,4897,84923,61463,40253,48073,73883,7123,95177,67549,9221,68513,93281,45907,58321,39071,17737,24121,31321,18427,92957,17497,22019,5441,47293,32671,31337,72221,79103,24253,17761,61483,83261,34253,88339,45979,34607,14719,18961,1811,22109,83701,12689,57737}

    {970,37545,37545,18552,37545,6478,37545,3266,37545,37545,37545,37545,37545,1930,37545,37545,661,37545,37545,37545,37545,37545,2071,13424,6224,691,37545,2551,15526,4899,37545,4874,6208,37545,37545,13292,2023,37545,37545,3292,37545,37545,2938,8107,18584,1325,15436,37545,12167,37545}

    Returns: 37545

  29. {49870,34493,76883,30983,39687,7367,21977,90371,29561,68417,43597,29299,98701,67043,58879,24917,15031,80471,18427,80993,35143,71503,63277,11327,58147,48347,39877,44843,81661,42589,5021,1123,11723,54533,10313,4099,36269,90791,88397,38243,38491,57671,74527,95177,58363,18457,21121,94999,41399,35107}

    {4420,19797,54290,23307,14603,2721,10336,54290,24729,54290,10693,24991,54290,54290,54290,4456,9197,54290,17436,54290,19147,54290,54290,8982,54290,5943,14413,9447,54290,11701,4080,386,7398,54290,2725,1003,18021,54290,54290,16047,15799,54290,54290,54290,54290,17376,12048,54290,12891,19183}

    Returns: 54290

  30. {16276,91811,5293,23695,90269,3169,47743,98221,42461,76509,46453,51407,76883,65063,13337,94099,3191,94847,64451,84079,73501,71371,43513,58727,26287,91697,97051,56993,29683,75629,94321,32399,98129,11689,3511,48149,30743,67307,35051,92779,66623,43601,17429,3581,55541,81841,5119,52571,66191,80209}

    {1064,33616,1858,9921,33616,1926,33616,33616,33616,33616,33616,33616,33616,33616,6942,33616,1706,33616,33616,33616,33616,33616,33616,33616,7329,33616,33616,33616,3933,33616,33616,1217,33616,10238,2017,33616,2873,33616,33616,33616,33616,33616,16187,1387,33616,33616,2902,33616,33616,33616}

    Returns: 33616

  31. {37533,70987,17650,95399,26629,34163,30169,19417,27617,24817,66869,53869,77879,68093,44309,54629,88807,86881,66089,13879,83719,93109,89653,69941,47897,36943,80809,80081,65063,1093,66431,94579,83921,62347,85961,1997,35597,87179,40163,26729,5323,2309,10709,21107,7219,17471,75913,34549,6067,80231}

    {5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,5949,484,5949,5949,5949,5949,5949,1955,5949,5949,5949,5949,626,1331,5949,5949,5949,5949,5949,5949,5949,5949}

    Returns: 5949

  32. {3390,71401,521,52531,37043,61471,64751,10321,14677,95503,45649,83663,1489,94799,38513,90551,76871,88817,80911,72983,80633,87877,68713,66289,13577,83179,75613,13147,33617,97081,36263,61559,3571,29251,45173,51043,80251,12049,48049,95881,52081,81901,41519,29027,78971,19259,59329,78979,2837,5353}

    {1855,1855,292,1855,1855,1855,1855,1855,1855,1855,1855,1855,366,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855,1855}

    Returns: 1855

  33. {71423,63374,43577,82311,89747,87391,43523,78845,33541,6277,24877,70417,85223,22987,87403,83627,50221,85451,92891,62297,73817,84361,66137,11359,4049,59809,56039,4993,16493,91529,74807,32603,84811,52313,43873,21493,17161,4007,70333,40709,5923,42563,16547,49901,59581,97043,65587,49339,16921,92377}

    {56939,56939,13362,56939,56939,56939,13416,56939,23398,446,7185,56939,56939,10965,56939,56939,6718,56939,56939,56939,56939,56939,56939,144,253,56939,900,2016,7460,56939,56939,24336,56939,4626,13066,13953,5456,841,56939,16230,3632,14376,7298,7038,56939,56939,56939,7600,6176,56939}

    Returns: 56939

  34. {28365,55217,90472,32411,8057,64859,94907,81811,55541,40811,71317,78899,29579,75017,64717,49481,58189,76037,24103,20981,78259,52879,68837,77771,58549,2329,93761,31543,36469,9859,2111,77111,83779,34351,66887,96133,89227,4583,90439,10457,60241,43259,66431,24001,26423,55873,52177,64577,78929,43487}

    {5694,34059,34059,1648,1831,34059,34059,34059,34059,34059,34059,34059,4480,34059,34059,34059,34059,34059,9956,13078,34059,34059,34059,34059,34059,1453,34059,2516,34059,4482,283,34059,34059,34059,34059,34059,34059,1978,34059,2688,34059,34059,34059,10058,7636,34059,34059,34059,34059,34059}

    Returns: 34059

  35. {42024,51083,79697,86447,81157,83809,89593,99497,74777,35845,98843,5063,92251,9923,46883,86197,91457,6311,9013,80587,72431,65167,60713,47653,60337,11897,99691,67363,86599,11131,79393,19753,50153,55261,93827,19979,80917,38809,3847,75151,30269,18407,17359,23719,53717,3529,67601,2539,75277,11383}

    {39713,39713,39713,39713,39713,39713,39713,39713,39713,3868,39713,4272,39713,21,39713,39713,39713,1847,3661,39713,39713,39713,39713,39713,39713,4022,39713,39713,39713,6320,39713,207,39713,39713,39713,19734,39713,904,1243,39713,9444,2899,4995,15994,39713,894,39713,1628,39713,5564}

    Returns: 39713

  36. {52357,68561,69023,30160,45089,32667,94051,92471,19439,86279,46049,1429,74707,91577,50123,28207,79873,14887,41467,93013,48403,41617,82021,26113,93349,94909,63787,62929,17737,25183,31877,91141,42919,31723,81703,21557,41729,49109,23929,19309,84919,50573,33923,1621,53689,70309,39511,80573,82001,23431}

    {15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,157,15876,15876,15876,15876,15876,989,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,15876,1287,15876,15876,15876,15876,15876,15876}

    Returns: 15876

  37. {6580,16151,67951,74717,33727,9319,15091,24317,39391,12583,52883,62813,55329,26951,45667,53783,97369,56279,82403,86027,48337,55661,14857,88841,98587,15647,3343,26869,30619,94267,96553,5477,66727,85513,1721,87209,9719,56893,19039,8689,9749,32749,11239,72889,95591,50387,62749,2623,37607,25793}

    {1860,3056,67660,67660,206,2427,7296,19026,28269,4745,14777,4847,12331,13758,21993,13877,67660,11381,67660,67660,19323,11999,8232,67660,67660,5072,800,13922,6422,67660,67660,1936,933,67660,541,67660,9346,10767,10543,6837,9166,2162,226,67660,67660,17273,4911,2085,30053,16074}

    Returns: 67660

  38. {69187,56632,44897,32321,74111,34347,95039,599,28309,98003,8725,17183,13847,92857,64529,23993,79939,99191,36427,21191,39679,71039,25901,51721,9133,49939,82879,36389,38411,19289,3257,97771,33407,733,67751,47903,60491,78853,40787,34169,14629,25303,48133,97547,95453,6331,38371,89899,95009,26629}

    {23978,36533,3371,28523,19054,24471,93165,320,8238,93165,5915,7250,10083,308,28636,21186,13226,93165,20311,8401,13807,22126,15462,41444,1835,43226,10286,20387,16343,16009,1969,93165,26351,74,25414,45262,32674,14312,11591,24827,5391,17256,45032,93165,93165,4531,16423,3266,93165,13278}

    Returns: 93165

  39. {34718,49699,9519,85127,44285,2047,86017,77489,81937,85363,59629,36371,4729,36773,23951,67559,62893,7583,43151,93319,14659,54239,21587,49729,523,26321,24091,3539,21391,83761,73387,94543,23867,75401,45043,25349,22567,37573,6551,59351,54679,85601,27883,99901,16309,67477,12827,19379,97303,85513}

    {25664,25664,6626,25664,25664,1100,25664,25664,25664,25664,25664,25664,2019,25664,1713,25664,25664,2915,25664,25664,11005,25664,4077,25664,37,25664,1573,891,4273,25664,25664,25664,1797,25664,25664,315,3097,25664,6011,25664,25664,25664,25664,25664,9355,25664,10,6285,25664,25664}

    Returns: 25664

  40. {4,99999}

    {0,1}

    Returns: 100000

  41. { 2, 10289, 73379, 42073, 49783, 18329, 3191, 65171, 65203, 92801, 34439, 48449, 81509, 2237, 3673, 49451, 64301, 373, 34429, 4783, 37871, 65963, 55673, 92387, 83101, 49177, 6863, 62477, 37691, 67511, 90173, 74131, 22531, 3221, 71329, 28927, 60107, 73477, 99017, 32653, 21067, 98081, 69941, 73079, 62189, 5261, 60017, 87427, 23537, 39839 }

    { 0, 7399, 26621, 15854, 434, 8355, 1079, 34829, 34797, 7199, 31122, 3102, 18491, 1572, 829, 1098, 35699, 36, 31142, 4340, 24258, 34037, 44327, 7613, 16899, 1646, 3918, 37523, 24618, 32489, 9827, 25869, 9876, 149, 28671, 13219, 39893, 26523, 983, 2041, 15732, 1919, 30059, 26921, 37811, 41, 39983, 12573, 5852, 20322 }

    Returns: 100000

  42. { 100, 1001 }

    { 0, 901 }

    Returns: 100000

  43. { 100000, 3 }

    { 0, 1 }

    Returns: 100000

  44. { 2, 3 }

    { 0, 0 }

    Returns: 0

  45. { 333, 100000 }

    { 100, 0 }

    Returns: 100000

  46. { 5, 11 }

    { 4, 5 }

    Returns: 49

  47. { 100000, 99999 }

    { 0, 1 }

    Returns: 100000

  48. { 11, 13, 17, 19, 23, 29, 31, 37, 41 }

    { 10, 4, 6, 3, 19, 8, 25, 26, 1 }

    Returns: 100000

  49. { 99999, 2 }

    { 1, 0 }

    Returns: 100000

  50. { 99999, 99997, 99995, 99991 }

    { 1, 3, 5, 9 }

    Returns: 100000

  51. { 99999, 99998 }

    { 1, 2 }

    Returns: 100000

  52. { 199, 197, 193, 191, 181, 179, 173, 167, 163, 157, 151, 149, 139, 137, 131, 127, 113, 109, 107, 103, 101, 97, 89, 83, 79, 73, 71, 67, 61, 59, 53, 47, 43, 41, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2 }

    { 102, 121, 26, 107, 88, 118, 6, 134, 81, 148, 38, 21, 59, 127, 47, 51, 108, 47, 62, 90, 10, 90, 53, 68, 65, 63, 32, 36, 21, 54, 42, 31, 25, 1, 26, 25, 8, 19, 3, 6, 4, 10, 5, 0, 1, 0 }

    Returns: 100000

  53. { 343, 1331, 2197, 4913, 6859, 12167, 24389, 29791, 50653, 68921, 79507 }

    { 221, 1026, 945, 3903, 3999, 1793, 13905, 8503, 38294, 38294, 38294 }

    Returns: 38294

  54. { 13, 17, 29, 31 }

    { 4, 6, 8, 25 }

    Returns: 100000

  55. { 3, 11, 13, 17, 19 }

    { 1, 10, 4, 6, 3 }

    Returns: 100000

  56. { 2, 3, 5 }

    { 0, 0, 0 }

    Returns: 0

  57. { 2, 3, 5, 7, 11, 13, 17 }

    { 0, 1, 0, 5, 10, 4, 6 }

    Returns: 100000

  58. { 5, 2 }

    { 3, 1 }

    Returns: 3

  59. { 2, 3 }

    { 1, 1 }

    Returns: 1

  60. { 3, 2 }

    { 1, 1 }

    Returns: 1

  61. { 49999, 2 }

    { 1, 0 }

    Returns: 50000

  62. { 99999, 100000 }

    { 1, 0 }

    Returns: 100000

  63. { 9, 13, 4 }

    { 1, 1, 1 }

    Returns: 1

  64. { 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 59, 61 }

    { 10, 4, 6, 3, 19, 8, 25, 26, 1, 25, 42, 54, 21 }

    Returns: 100000

  65. { 3, 4 }

    { 0, 0 }

    Returns: 0

  66. { 91921, 93889 }

    { 8079, 6111 }

    Returns: 100000

  67. { 99991, 2 }

    { 9, 0 }

    Returns: 100000

  68. { 99999, 10 }

    { 1, 0 }

    Returns: 100000

  69. { 2, 3, 5 }

    { 1, 1, 1 }

    Returns: 1

  70. { 100000, 99999, 99997, 79, 37 }

    { 19, 19, 19, 19, 19 }

    Returns: 19

  71. { 2, 5 }

    { 0, 0 }

    Returns: 0

  72. { 343, 1331, 2197, 4913, 6859, 12167, 24389, 29791, 50653, 68921, 79507, 2 }

    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    Returns: 0

  73. { 2, 5 }

    { 1, 1 }

    Returns: 1

  74. { 5, 13 }

    { 2, 3 }

    Returns: 42

  75. { 3, 5, 7 }

    { 2, 4, 6 }

    Returns: 104

  76. { 3, 50000 }

    { 1, 0 }

    Returns: 100000

  77. { 5, 7 }

    { 0, 0 }

    Returns: 0

  78. { 50, 99999 }

    { 0, 1 }

    Returns: 100000

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