Statistics

Problem Statement for "OrderedNim"

Problem Statement

Nim is a game in which two players take turns removing stones from heaps. On each turn, a player must choose a single heap and remove one or more stones from that heap. The player who takes the last stone wins.

Alice and Bob are bored with playing Nim over and over again, so they've decided to create a new variation called Ordered Nim. Ordered Nim differs from regular Nim in the following way. The heaps are numbered 0 through n-1 (where n is the number of heaps), and a player can only remove stones from a heap if all the lower-numbered heaps are empty.

You are given a int[] layout, where the i-th element (0-indexed) is the number of stones in heap i at the beginning of the game. Alice will take the first turn. Determine who will win the game, assuming both players play optimally. Return "Alice" if Alice will win, or "Bob" if Bob will win (all quotes for clarity).

Definition

Class:
OrderedNim
Method:
winner
Parameters:
int[]
Returns:
String
Method signature:
String winner(int[] layout)
(be sure your method is public)

Constraints

  • layout will contain between 1 and 50 elements, inclusive.
  • Each element of layout will be between 1 and 1000000000, inclusive.

Examples

  1. {5}

    Returns: "Alice"

    Alice takes all 5 stones and wins.

  2. {1,2}

    Returns: "Bob"

    According to the rules of the game, Alice is not allowed to take stones from heap 1 because heap 0 is not empty. Her only option is to take the one stone from heap 0. Heap 0 will then be empty, so Bob can take both stones from heap 1 to win the game.

  3. {2,1}

    Returns: "Alice"

  4. {10,9,8,7,6,5,4,3,2,1}

    Returns: "Alice"

  5. {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000};

    Returns: "Alice"

  6. {1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000};

    Returns: "Bob"

  7. {1,1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000};

    Returns: "Alice"

  8. {1,1,1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000};

    Returns: "Bob"

  9. {1,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1};

    Returns: "Bob"

  10. {1}

    Returns: "Alice"

  11. {1,1}

    Returns: "Bob"

  12. {1,1,1}

    Returns: "Alice"

  13. {1,1,1,1}

    Returns: "Bob"

  14. {1,1,1,1,1}

    Returns: "Alice"

  15. {1,1,1,1,1,1}

    Returns: "Bob"

  16. {1,1,1,1,1,1,1}

    Returns: "Alice"

  17. {1,1,1,1,1,1,1,1}

    Returns: "Bob"

  18. {1,1,1,1,1,1,1,1,1}

    Returns: "Alice"

  19. {1,1,1,1,1,1,1,1,1,1}

    Returns: "Bob"

  20. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Alice"

  21. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Bob"

  22. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Alice"

  23. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Bob"

  24. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Alice"

  25. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Bob"

  26. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Alice"

  27. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Bob"

  28. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Alice"

  29. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: "Bob"

  30. {1,1,1,1,1,1,2,2,2,1,2,1,1,2,1,1,1,2,2,2}

    Returns: "Alice"

  31. {1,1,1,1,1,2,1,1,1,1,2,1,2,1,1,1,1,1,1,2,2,1}

    Returns: "Bob"

  32. {1,1,1,1,1,1,2,1,2,1,1,1,2,2,1}

    Returns: "Alice"

  33. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,2,2,2,1,2,1,1,2,1,1,1,1,1}

    Returns: "Alice"

  34. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,1,1,2,1,1}

    Returns: "Alice"

  35. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,1,2,1,2,2,1,2,2,1,2,2,2,2,1,1,2}

    Returns: "Alice"

  36. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,2,1,2}

    Returns: "Alice"

  37. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,2,1,1}

    Returns: "Bob"

  38. {1,1,1,1,2,2,2,1,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,2,2,2,1}

    Returns: "Alice"

  39. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,2,1,2,1,1,1,1,1,1,1}

    Returns: "Alice"

  40. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,947537006,722267024,466906117,324990703,545986140,317216041,558508476,828919417,837043944,373071872,413208632,58005784,53475677,695493399,913354089,480216984,520553320,913264590,56884446,47157704,75516531,127664223,327078476,705449376}

    Returns: "Alice"

  41. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,896565404,584001868,367826018,887842897,128116527,167879376,610109921,447538995,345386430,8612412,764755035,903894905,837531828,454315330,129483128,103256811,512321114,182958804,798750209,278191554,663175787,171819880,43972496,720060232,71493936}

    Returns: "Bob"

  42. {398572411,677454754,915652074,309340605,426536509,352170293,677166623,314379405,480286819,697562350,777005677,927825814,42948779,785618088,545097200,799360035,475666267,851928882,928843162,578923078,216766347,111801965,230189638,494957900,627494103,402009518,391446747,200070686,473503453,510935773,900311492,872075863,40906878,668479917,181416467,467443386,20650209,711099441,781822790,353453379}

    Returns: "Alice"

  43. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,133795544,304126920,196962906,678892744,103486954,672629173,383337977,32330115,104068602,600104323,996648431,334258239,95062222,624142533,736267756,339025321,824213219,209771208,849961093,577041062,81847070,890867970,98037330,115779889,210827707,118687538}

    Returns: "Alice"

  44. {1,1,1,472140916,88057471,256511666,605936460,392184390,453474572,137345555,348187696,978620096,520683531,233034162,82688697,120787853,229682593,416946935,68366426,706341477,5731043,259908098,383071047,215502250,109869190,960112108,149865672,853253511,58149437,118161912,64081217,29353326,945041240,909248065,354010594,885615062,18276082,959947053,130315804,471750653}

    Returns: "Bob"

  45. {1,1,1,1,1,1,1,1,302887100,323008841,711537660,385575796,296313045,941220252,655039083,217195822,500078081,660770125,477103920,883149127,876272374,439489461,695777587,878654397,145259324,606443375,996816308,61856892,635796701,794373900,971104956,989807294,679988961,989381038,802270698,810304764,313648042,604596008,141324614,616535142}

    Returns: "Alice"

  46. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,854627289,223917892,646598877,509666371,441113713,146676957,22952847,918217632,29826084,899225221,210223445,578120022,630395969,355482768,184563396,627212277,417339659,672876448,274102528,240960967,515200093,954091488,82858356,169987142}

    Returns: "Alice"

  47. {1,1,1,774583149,758237217,865557890,702187996,463615842,720185179,778622239,110214719,82367901,72252304,109408027,105320748,990469935,139234110,857062320,53209731,569870483,487458288,408692498,754433879,967186916,826032157,279826678,241289443,66993123,795026771,47897283,149851478,965013912,517326238,398874226,739597061,128079806,264432116,294301408,591695648,837133646}

    Returns: "Bob"

  48. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,919501546,145175950,811318392,877338645,988162236,803068854,734400964,41371967,225455688,74375604,302580816,979889566,41562519,128612972,112232596,135368314,48122446,907259366,35781948}

    Returns: "Bob"

  49. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,553108185,596848149,464386689,681187990,713796616,611204449,272883637,550930261,536644447,827310354,322948158,534336748,491145098,52803155,375015335,146730303,787204118,268903653}

    Returns: "Alice"

  50. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,571484469,204591908,608174944,700097440,316824503,743543257,748219886,224083868,779325204,798710160,948873496,184949740,248074660,265776537,866137729,961871275,876980985,139021366,365317887,413625431,818848071,688266045,947962178,309993168,741069199,175493864}

    Returns: "Alice"

  51. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,444397517,828909460,94885741,15881985,33501367,555577036,568495776,202842221,151636644,169232013,426926088,930961847,967942173,228315935,115911586,216016832,494092471,834565666,30404459,371073455,826103383}

    Returns: "Bob"

  52. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,644951454,83988389,437693766,807460973,677573939,613187630,116700795,910879959,57585146,945610254,858282051,73467130,831627972,413859086,494479257,34470192,565495729,663711270,313912631,348973927,631653442}

    Returns: "Bob"

  53. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,700186625,36321036,4483881,730591083,259910842,830587264,126313428,897126079,328055069,62818168,187336196,135516041,592908459,800523825,252216835,503788417,858108970,50343440,214586819,784092451,734487763,628445904,131088060,621474306,46457984,794799329}

    Returns: "Alice"

  54. {1,1,1,1,1,1,1,1,1,1,278969122,330131853,565350125,979155746,218969240,569834005,709746829,331396433,252937620,688576608,81038863,580992688,751394775,268375059,716508729,196819585,68898883,821241915,700608001,779524205,871585355,915194819,416133007,458589469,396157074,547221066,80063775,295131409,342020394,867967062}

    Returns: "Alice"

  55. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,50615266,108429794,452661613,269584505,530780151,14924793,600980938,783717770,703501400,682019800,217226810,307412526,950394858,933735538,504232111,871810093,607493804,57356463,651334297,331595510,972551282}

    Returns: "Bob"

  56. {1,1,221224707,467204721,870248753,516356116,809225114,590732166,59435785,282730981,641347432,20381931,735392593,910931936,403678433,750317385,364429225,39912554,306335136,898965377,257139363,613747661,701876586,43391252,117979771,573686678,650885056,175336234,77537326,982480565,403867,997520981,625181895,74144925,464725701,347946999,590501040,126467166,938679165,502453177}

    Returns: "Alice"

  57. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,375351459,997107090,343474883,631546243,599940826,560420460,671458796,906275961,459385836,781114511,372539974,13778773,824505762,490519744,587465451,327907169,518372329,517519128,162904086,518776195,515040108}

    Returns: "Alice"

  58. {1,1,1,1,832282160,136032979,35938511,958749326,927228495,390908039,72980175,359771442,766259497,70087265,703246324,250322091,522544442,116183135,921780887,281336755,575568970,555411749,653876728,589347743,232433862,996912823,29329545,560341031,515285152,546848672,575761468,886577698,914405132,216363799,332015169,746687291,204913129,367953680,557952968,132141623}

    Returns: "Alice"

  59. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,491913064,377637567,553536759,47675740,627959657,928597552,163858874,402256895,62450658,591944196,957668643,716327385,33808290,42618857,565756560,63137834,602959887,81041711,462502857,31237706,820135760,376907988,247601504}

    Returns: "Bob"

  60. {1,1,1,452514633,372620960,386580950,584656255,131482677,17514092,929085671,361636595,423567202,976761410,842112604,204681106,993136635,96885850,267131763,585080830,54554493,983459148,618889119,97173349,401732059,534543304,552649587,335290121,997046161,583887292,155425880,226470500,831488795,160093160,202582130,136519779,532714119,589163080,721176034,516713148,459193523}

    Returns: "Bob"

  61. {1,1,1,1,1,735277077,332055817,572978697,939958182,325192451,669864547,207089944,762789633,576935391,43065443,234195103,526625091,444797501,768738407,79274677,780087621,765784567,515678320,788029853,992255066,199683466,948123012,47353548,336203245,480837131,489032979,909895630,997550278,948226501,412673685,728416371,536019929,744729501,153911420,475978110}

    Returns: "Bob"

  62. {1,1,535584406,685227935,400711356,578649848,919423038,927336446,875963701,540677796,859127474,508567673,158978714,227322145,296597525,3750131,279521962,97236889,51103678,615725206,578074019,540136656,378137187,428140648,340879509,790810871,9073370,876899437,388056723,162984789,205393899,163011378,986760754,740978304,848239312,239988461,172144503,620178701,19841258,48108203}

    Returns: "Alice"

  63. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,409192228,172351561,958807227,705789752,176101692,90845541,803026640,227205369,706570746,233617010,619858377,84707933,514274009,960737885,728035155,523347379,690153673,968608230}

    Returns: "Alice"

  64. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,131619607,378125625,341558578,832375270,618114085,513703081,305070323,490471695,414327635,318443170,221956777,823519862,490794731,33280356,381825966,666896422,124125896,37368957,894101790,683212993,123502319,366476518,620437277}

    Returns: "Alice"

  65. {1,200988784,13640057,869884427,169597013,552488576,470464701,153732971,930614200,812023279,986108240,401244636,178242711,291178562,891716330,592570345,609621732,113673107,268606559,100416462,999469814,502948876,619829235,123595709,540317832,366447376,659325053,663820150,732923894,279762330,154112829,912654647,480751113,167752885,635055425,502864477,720241460,105520126,656597447,650855659}

    Returns: "Bob"

  66. {1,1,1,52100295,95786114,786400600,796332976,540872810,248538683,762522434,661995720,201471496,761992247,164944595,821300730,738104307,557778779,187748105,249945712,74115280,920671998,529708041,228228108,685842997,862975505,395980993,320898421,365839981,116222452,278934898,22437427,619594463,48994653,517659464,524211109,144780766,156576415,320544084,538169928,405115097}

    Returns: "Bob"

  67. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,606586592,697575116,217626594,427887321,288195775,775405372,468151778,538141486,849520651,241340127,920365878,77748759,927183123,783341382,326246103,100597896,1697714,442468554,379532793,876651492,62063016,428527446,246827307,438790476}

    Returns: "Bob"

  68. {1,1,1,1,1,1,1,1,1,1,1,1,759334560,963994490,808518818,694917429,16676489,415105410,245008896,86819434,695509082,385721022,714741157,163660859,923862507,416778159,405000986,696744736,347043269,184700460,332602469,673289371,285298355,334300182,115757925,664831148,63468025,30337292,93358593,310295332}

    Returns: "Alice"

  69. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,713699053,80978679,335693997,522217870,628412459,204886837,789839631,725937706,144222622,485348713,111658728,858963778,501525923,888037586,275741936,906526908,584782322,622785205,91227368,917384790,148590927}

    Returns: "Bob"

  70. {1,187105356,945528227,113794062,564088802,232419911,724800536,60979871,87522511,875646127,169760475,637192841,797512818,138477112,145474318,807396585,484434917,869052546,694048563,17456020,480458418,401188913,941643840,614089334,328438359,372040994,544030759,80735903,146581513,60179865,521029894,11187850,247285220,319074472,124981911,811374022,551494383,849782446,872353892,639016893,577944924,42114367,128726085,375457741,33107830,274200402,35370677,517542746,995769299}

    Returns: "Bob"

  71. {1,328744068,130608152,329158957,942833402,311562862,701199950,339380512,244815116,700297815,399560377,765845009,711485664,646845596,84919481,836467574,310735969,488930215,686250019,35606213,127947107,116711294,930236931,109189543,492169034,963344760,235906296,527539710,480887505,231675594,109475301,15886269,560419662,92599805,197561577,355769415,404162666,898761527,695149926,648977782,599059341,94710302,267339142,163061356,594072250,204774974,999528929,904808218,693705188}

    Returns: "Bob"

  72. {674168646,655006592,723167712,635874540,147175625,539028823,871780835,527231686,19916327,103456429,489223339,888318948,516392442,581823143,85880524,872161856,838502160,837158402,419828133,339996293,288734094,514538435,607335435,451795449,108610684,664626760,451324377,865935253,210848300,989619675,511382387,885016945,497142618,87066450,373407837,496834594,626095273,245188671,24066280,498527951,201161451,365805970,239363250,570070244,947629112,177760126,294748451,638647623,14918527}

    Returns: "Alice"

  73. {1,303652621,81631370,438495702,755448069,42758405,103122461,59288798,908693657,313970760,901424824,272592395,51504057,398567442,359658845,424911893,895402035,985754117,522616915,771984666,484282067,723778366,137790635,723645317,146364961,937936098,901405442,441113412,429100073,768840320,155689995,407743988,72492940,237321364,846239689,680457361,280079768,801878501,592262510,41289776,115849261,493687333,313882171,19869669,744771126,673541015,297297913,492689513,511811483}

    Returns: "Bob"

  74. {996093549,396209544,107497517,572255217,542574505,45433614,326177010,983687916,327050038,95017330,139377910,734794025,20026621,229215625,433550065,553000333,361811744,87944918,145262842,403101519,56310530,491466527,569500041,76180198,88754004,95557407,373478110,581443516,607368889,45909288,698634046,455978790,442118832,806131562,28234006,984693336,704081527,206927368,968381251,31131565,154461049,960275512,618441941,27004021,42007488,51992006,432520706,403819231,139936923}

    Returns: "Alice"

  75. {48763804,921766425,228937142,124944001,10520429,324494548,350938462,444480296,931863437,396847749,143114341,240358578,838966580,949245902,121108935,823659915,505843781,328036302,644557517,536975345,335013702,457349380,7933637,362017723,351873219,59925642,794538428,755692449,52378916,77354678,267645902,101142719,999121103,496583043,78603071,862157883,673593942,429541532,159154530,457973730,826389281,302268871,698332307,517872212,104031124,819441242,194048479,609874904,147477543}

    Returns: "Alice"

  76. {335007597,148471727,7300237,697025319,500344945,919742230,344080098,108553746,824637498,421434775,376199647,778296568,273072229,725299041,856899639,987746463,398892982,138957522,146900993,856866712,817863154,301686215,407715370,335735366,405717338,227156611,529783844,868108594,227150506,220906190,867475193,562158102,221894268,727291781,111699772,722239213,647034011,308296221,683309310,324187860,729730995,59508956,102484427,855319576,637324348,811900417,843066038,36217329,950857939}

    Returns: "Alice"

  77. {1,621237444,144169596,5832114,956972809,402403286,232988724,339273004,270511879,312655581,412695546,990503423,874813682,634589813,717795204,839029805,209345377,217345566,147326025,892654686,541533425,729573372,804679993,496534203,584892947,442004340,308434620,280475336,330738021,111808910,122958718,928854764,733046353,119644665,934686877,542535514,522047950,20191953,734324869,645076180,332847533,147020414,635579603,60177567,781610227,205891158,899207371,990955603,275753075}

    Returns: "Bob"

  78. {1,817286499,628623119,540806633,166337053,66032417,835327325,474771672,346507752,18581697,439096933,321982821,947436460,24659638,294143838,882123337,567195151,816191787,902315289,154036371,313784319,87679173,301056785,949363921,147856739,935183363,7771430,47064110,778655317,283524504,946113857,514781957,953327354,574736975,908104942,119664406,640769391,743432266,446952430,839793494,762013962,886049362,14292667,561966773,910708999,308436504,296606461,330420501,124628290}

    Returns: "Bob"

  79. {290928960,139117274,785513656,92809232,286974012,573213370,100580661,334038121,351868686,236621516,132668329,719166995,189948869,707405303,627271936,162129627,200691045,223220553,609082056,40484539,837750866,495131417,54777205,399717638,258356768,215730060,696324099,588777268,192874701,747762199,73234139,483803661,886879472,711264146,576612892,26369836,284477515,677193553,360407956,488862553,913815068,493076285,208029547,956280289,52997939,687817834,118409915,106205336,911038386}

    Returns: "Alice"

  80. {10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }

    Returns: "Alice"

  81. {2, 1, 1 }

    Returns: "Alice"

  82. {5 }

    Returns: "Alice"

  83. {1, 2 }

    Returns: "Bob"

  84. {999999951, 999999952, 999999953, 999999954, 999999955, 999999956, 999999957, 999999958, 999999959, 999999960, 999999961, 999999962, 999999963, 999999964, 999999965, 999999966, 999999967, 999999968, 999999969, 999999970, 999999971, 999999972, 999999973, 999999974, 999999975, 999999976, 999999977, 999999978, 999999979, 999999980, 999999981, 999999982, 999999983, 999999984, 999999985, 999999986, 999999987, 999999988, 999999989, 999999990, 999999991, 999999992, 999999993, 999999994, 999999995, 999999996, 999999997, 999999998, 999999999, 1000000000 }

    Returns: "Alice"

  85. {1, 1, 1000000000, 1000000000, 1, 2, 1000000000, 1, 1, 1000000000 }

    Returns: "Alice"

  86. {3, 1, 3, 1 }

    Returns: "Alice"

  87. {1, 1000000000, 1, 1, 1, 1000000000, 1, 1000000000, 1, 1, 1, 1 }

    Returns: "Bob"

  88. {1 }

    Returns: "Alice"

  89. {1, 1, 1 }

    Returns: "Alice"

  90. {1, 1, 1, 1, 1 }

    Returns: "Alice"

  91. {3, 1 }

    Returns: "Alice"

  92. {2, 1, 2, 2 }

    Returns: "Alice"

  93. {2, 2 }

    Returns: "Alice"

  94. {2, 1, 2 }

    Returns: "Alice"

  95. {10, 1, 10 }

    Returns: "Alice"

  96. {1, 2, 1, 10, 10 }

    Returns: "Bob"

  97. {1, 1, 4, 1, 4 }

    Returns: "Alice"

  98. {1, 2, 1 }

    Returns: "Bob"

  99. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

    Returns: "Alice"

  100. {1, 1, 2, 2 }

    Returns: "Alice"

  101. {3, 1, 2 }

    Returns: "Alice"

  102. {1, 1 }

    Returns: "Bob"

  103. {1, 5, 1, 1 }

    Returns: "Bob"

  104. {2, 2, 2 }

    Returns: "Alice"

  105. {1, 2, 3 }

    Returns: "Bob"

  106. {1, 1, 1, 1 }

    Returns: "Bob"

  107. {2, 2, 1, 2 }

    Returns: "Alice"

  108. {3, 5 }

    Returns: "Alice"

  109. {2, 1, 1, 1, 1 }

    Returns: "Alice"

  110. {2, 1, 1, 1, 2 }

    Returns: "Alice"

  111. {2, 1 }

    Returns: "Alice"

  112. {1, 1, 2, 2, 1, 2 }

    Returns: "Alice"

  113. {7, 1, 2, 6 }

    Returns: "Alice"

  114. {5, 5, 1, 5, 5 }

    Returns: "Alice"

  115. {3, 4 }

    Returns: "Alice"

  116. {1, 1, 1, 2, 1, 1 }

    Returns: "Bob"

  117. {8, 1, 5 }

    Returns: "Alice"

  118. {3, 1, 3 }

    Returns: "Alice"

  119. {1, 2, 1, 2, 1 }

    Returns: "Bob"

  120. {1, 1, 3, 1, 2 }

    Returns: "Alice"

  121. {3, 2 }

    Returns: "Alice"

  122. {1, 1, 2, 1, 1 }

    Returns: "Alice"

  123. {2, 2, 1, 2, 1, 1, 1 }

    Returns: "Alice"

  124. {1, 1, 2 }

    Returns: "Alice"

  125. {3, 3 }

    Returns: "Alice"

  126. {1, 1, 1, 2, 2 }

    Returns: "Bob"

  127. {2, 1, 2, 1 }

    Returns: "Alice"

  128. {3, 1, 1, 3 }

    Returns: "Alice"

  129. {1, 3, 2, 2, 3 }

    Returns: "Bob"

  130. {2, 3 }

    Returns: "Alice"

  131. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

    Returns: "Alice"

  132. {1, 2, 3123456 }

    Returns: "Bob"

  133. {1, 2, 1, 2 }

    Returns: "Bob"

  134. {262236773, 208042610, 800207363, 428428950, 47718729, 793958356, 543227092, 255063702, 245922718, 448084511, 841298077, 50803248, 489249764, 634882133, 437249776, 192858939, 769723076, 17244080, 451954760, 998335073, 962932683, 107998841, 117154511, 343955363, 434512597, 123907814, 495496907, 546733314, 503129484, 176639951, 280148755, 367267899, 454227564, 981534503, 520949728, 114045555, 185760391, 671248907, 815949939, 909681830, 282187155, 589192792, 614643670, 338765782, 328686463, 295108507, 673893159, 736913846, 137660168, 555815228 }

    Returns: "Alice"

  135. {1, 2, 1, 1 }

    Returns: "Bob"

  136. {3, 1, 2, 2 }

    Returns: "Alice"

  137. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

    Returns: "Alice"

  138. {3, 1, 1 }

    Returns: "Alice"

  139. {1000000, 9, 8, 700000, 6, 5, 4, 3, 2, 1, 600 }

    Returns: "Alice"

  140. {1, 5, 1, 1, 1 }

    Returns: "Bob"

  141. {1, 3, 4 }

    Returns: "Bob"

  142. {10, 10 }

    Returns: "Alice"

  143. {10, 1, 1, 1, 1 }

    Returns: "Alice"

  144. {2, 1000 }

    Returns: "Alice"

  145. {1, 1, 2, 1, 2 }

    Returns: "Alice"

  146. {2, 10 }

    Returns: "Alice"

  147. {3, 1, 3, 3 }

    Returns: "Alice"

  148. {4, 1, 2 }

    Returns: "Alice"

  149. {7, 4, 1, 6, 10 }

    Returns: "Alice"

  150. {7, 1, 6, 1, 5, 1, 8 }

    Returns: "Alice"

  151. {1010000, 91000, 81000, 7, 6, 5, 4, 3, 2, 1, 10, 10, 10, 100, 10, 10, 10, 10, 10, 1000, 1000000, 1, 10000000, 100000000, 10000, 1000000, 10000000, 10000, 1000, 1000, 1, 10000, 1000, 1000, 1000, 100, 1000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000 }

    Returns: "Alice"

  152. {3, 1, 1, 1, 2 }

    Returns: "Alice"

  153. {6, 6, 6 }

    Returns: "Alice"

  154. {5, 5, 1, 5 }

    Returns: "Alice"

  155. {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

    Returns: "Alice"

  156. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000 }

    Returns: "Alice"

  157. {3, 5, 2 }

    Returns: "Alice"

  158. {3, 1, 2, 1 }

    Returns: "Alice"

  159. {2 }

    Returns: "Alice"

  160. {10, 1, 1 }

    Returns: "Alice"

  161. {1, 1, 1, 2, 1 }

    Returns: "Bob"

  162. {1000000, 1000000, 3, 3 }

    Returns: "Alice"

  163. {10, 10, 10 }

    Returns: "Alice"

  164. {5, 1, 1, 1, 1 }

    Returns: "Alice"

  165. {5, 4 }

    Returns: "Alice"

  166. {1, 1, 3, 1 }

    Returns: "Alice"

  167. {1, 1, 2, 1, 1, 1 }

    Returns: "Alice"

  168. {1, 4, 4, 4 }

    Returns: "Bob"

  169. {5, 1, 1 }

    Returns: "Alice"

  170. {2, 1, 1, 2, 1, 3 }

    Returns: "Alice"

  171. {1, 1, 1, 3, 2 }

    Returns: "Bob"

  172. {1, 1, 1, 1, 2, 1, 1, 1, 2 }

    Returns: "Alice"

  173. {1, 1, 4, 1, 1 }

    Returns: "Alice"

  174. {43, 3, 4, 4, 3, 6, 3, 42, 2, 1, 12, 2, 1, 2, 3, 4, 2 }

    Returns: "Alice"

  175. {4, 1, 2, 1 }

    Returns: "Alice"

  176. {1, 2, 3, 1, 1, 1 }

    Returns: "Bob"

  177. {1, 1, 999999999, 1, 1 }

    Returns: "Alice"

  178. {1, 2, 2 }

    Returns: "Bob"

  179. {5, 3 }

    Returns: "Alice"

  180. {1, 2, 2, 1, 1 }

    Returns: "Bob"

  181. {1, 3, 1, 1 }

    Returns: "Bob"

  182. {1, 4, 1, 1, 1 }

    Returns: "Bob"

  183. {2, 4 }

    Returns: "Alice"

  184. {2, 3, 1 }

    Returns: "Alice"

  185. {1, 1, 17, 1 }

    Returns: "Alice"

  186. {16, 1, 1, 1, 13414 }

    Returns: "Alice"

  187. {1, 1, 1, 1, 2 }

    Returns: "Alice"

  188. {1, 1, 1, 100, 1, 1 }

    Returns: "Bob"

  189. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1, 1000000000 }

    Returns: "Alice"

  190. {2, 1, 1, 1 }

    Returns: "Alice"

  191. {2, 2, 1, 1 }

    Returns: "Alice"

  192. {3, 5, 2, 3, 1, 1, 1, 2 }

    Returns: "Alice"

  193. {1, 2, 2, 1, 2 }

    Returns: "Bob"

  194. {1, 5, 1, 5 }

    Returns: "Bob"

  195. {1110, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 114, 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 }

    Returns: "Alice"

  196. {2, 1, 8 }

    Returns: "Alice"

  197. {1, 5, 1 }

    Returns: "Bob"

  198. {1, 1, 1, 1, 2, 1, 1, 1, 1 }

    Returns: "Alice"

  199. {1, 1, 1, 2 }

    Returns: "Bob"

  200. {5, 5, 4, 6 }

    Returns: "Alice"

  201. {1, 1, 5, 1, 1 }

    Returns: "Alice"

  202. {2, 3, 3, 3 }

    Returns: "Alice"

  203. {1, 3, 1, 2, 2, 2 }

    Returns: "Bob"

  204. {1, 1, 1, 2, 1, 1, 1, 1 }

    Returns: "Bob"

  205. {1, 1, 3, 1, 2, 3 }

    Returns: "Alice"

  206. {1, 1, 2, 1 }

    Returns: "Alice"

  207. {1, 1, 1, 1, 2, 1, 1 }

    Returns: "Alice"

  208. {2, 3, 4, 5, 1, 2, 2, 2, 2, 1, 1, 2, 1 }

    Returns: "Alice"

  209. {3, 4, 2, 1 }

    Returns: "Alice"

  210. {2, 2, 1, 1, 2 }

    Returns: "Alice"

  211. {2, 1, 1, 1, 3 }

    Returns: "Alice"

  212. {5, 10, 15 }

    Returns: "Alice"

  213. {3, 3, 1, 2 }

    Returns: "Alice"

  214. {5, 1, 1, 1, 3, 1 }

    Returns: "Alice"

  215. {2, 100, 1 }

    Returns: "Alice"

  216. {1, 2, 5, 1, 3, 2 }

    Returns: "Bob"

  217. {1, 1, 1, 1, 1, 1, 1 }

    Returns: "Alice"

  218. {5, 5 }

    Returns: "Alice"

  219. {1, 4, 1, 1, 1, 1 }

    Returns: "Bob"

  220. {1, 3, 3 }

    Returns: "Bob"

  221. {2, 3, 4, 5 }

    Returns: "Alice"

  222. {4, 4, 4, 4 }

    Returns: "Alice"

  223. {3, 1, 1, 1 }

    Returns: "Alice"

  224. {87, 8, 687, 68, 76, 876, 8687, 6 }

    Returns: "Alice"

  225. {1, 5, 8 }

    Returns: "Bob"

  226. {1, 1, 1, 2, 1, 2 }

    Returns: "Bob"

  227. {2, 5, 1 }

    Returns: "Alice"

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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