Statistics

Problem Statement for "ProductsOfDigits"

Problem Statement

Given a positive integer N, let P(N) denote the product of all digits in the decimal representation of N. For example, P(4256) = 4 * 2 * 5 * 6 = 240, P(2112) = 2 * 1 * 1 * 2 = 4 and P(100) = 1 * 0 * 0 = 0.

Consider the infinite sequence S = (P(1), P(2), P(3), ...). Given a int[] prod containing exactly M elements, find the first occurrence of (prod[0], prod[1], ..., prod[M-1]) in S as a consecutive subsequence. In other words, return the smallest positive index X such that P(X + i) = prod[i] for all i between 0 and M-1, inclusive. The constraints will guarantee that at least one such X exists.

Definition

Class:
ProductsOfDigits
Method:
firstOccurrence
Parameters:
int[]
Returns:
long
Method signature:
long firstOccurrence(int[] prod)
(be sure your method is public)

Notes

  • It can be shown that under the constraints of this problem, the return value will always fit within a 64-bit signed integer datatype.

Constraints

  • prod will contain between 1 and 50 elements, inclusive.
  • Each element of prod will be between 0 and 1,000,000,000, inclusive.
  • There will be at least one occurrence of (prod[0], ..., prod[M-1]) in S as a consecutive subsequence, where M is the number of elements in prod.

Examples

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

    Returns: 1

    Since P(1) = 1, P(2) = 2, ..., P(5) = 5, we have that S starts with an occurrence of (1, 2, 3, 4, 5).

  2. {9, 0, 1}

    Returns: 9

    P(9) = 9, P(10) = 0, P(11) = 1.

  3. {0, 0, 0, 0}

    Returns: 100

    All numbers between 100 and 103, inclusive, have a 0 in their decimal representations.

  4. {288}

    Returns: 489

    4 * 8 * 9 = 288.

  5. {108864, 127008, 145152, 163296, 0, 22680, 45360, 68040, 90720}

    Returns: 789946

  6. {157464}

    Returns: 389999

  7. {1}

    Returns: 1

  8. {0, 1, 2, 3, 4, 5}

    Returns: 10

  9. {0}

    Returns: 10

  10. {0,0}

    Returns: 100

  11. {0,0,0,0,0,0,0,0,0,0,0}

    Returns: 100

  12. {0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 1000

  13. {0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0}

    Returns: 1000

  14. {0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0}

    Returns: 1000

  15. {244140625}

    Returns: 555555555555

  16. {0,244140625}

    Returns: 5555555555550

  17. {0,0,0,0,0,0,0,0,0,0,0,0,244140625}

    Returns: 555555555555099

  18. {0,0,0,0,0,0,0,0,0,0,0,244140625}

    Returns: 55555555555500

  19. {0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,488281250}

    Returns: 2555555555555062

  20. {75600000,90720000,105840000,120960000,136080000,0,17010000,34020000,51030000,68040000,85050000,102060000,119070000,136080000,153090000,0,0,0,0,0,0,0,0,0,0,0,3780000,7560000,11340000,15120000,18900000,22680000,26460000,30240000,34020000,0,7560000,15120000,22680000,30240000,37800000,45360000,52920000}

    Returns: 55556789185

  21. {8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8}

    Returns: 8

  22. {27,0}

    Returns: 39

  23. {0,0,0,0,0,0,0,0,0,0,4147200,8294400,12441600,16588800,20736000,24883200}

    Returns: 4558889901

  24. {5103000,6123600,7144200,8164800,9185400,0,1224720,2449440,3674160,4898880,6123600,7348320,8573040,9797760,11022480,0,1428840,2857680,4286520,5715360,7144200,8573040,10001880,11430720,12859560,0,1632960,3265920,4898880,6531840,8164800,9797760,11430720,13063680,14696640}

    Returns: 57899955

  25. {5644800,6451200,7257600,0,907200,1814400,2721600,3628800,4536000,5443200,6350400,7257600,8164800,0,0,0,0,0,0,0,0,0,0,0,120960,241920,362880,483840,604800,725760,846720,967680,1088640,0,241920,483840,725760,967680,1209600,1451520,1693440,1935360,2177280,0,362880,725760}

    Returns: 57889587

  26. {0,0,0,0,0,0,0,0,0,0,6,12,18,24,30,36,42,48,54,0,12,24,36,48,60,72,84,96,108}

    Returns: 601

  27. {4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8,12,16}

    Returns: 4

  28. {48620250,58344300,68068350,77792400,87516450,0,11344725,22689450,34034175,45378900,56723625,68068350,79413075,90757800,102102525,0,12965400,25930800,38896200,51861600,64827000,77792400,90757800,103723200,116688600,0,14586075,29172150,43758225,58344300,72930375,87516450,102102525}

    Returns: 3557777965

  29. {2700,3240}

    Returns: 25695

  30. {3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21}

    Returns: 3

  31. {10800,14400,18000,21600,25200,28800,32400,0,4200,8400,12600}

    Returns: 355863

  32. {32,48,64,80}

    Returns: 282

  33. {4423680,6635520,8847360,11059200,13271040,15482880,17694720,19906560,0,2488320,4976640,7464960,9953280,12441600,14929920,17418240,19906560,22394880,0,0,0,0,0,0,0,0,0,0,0,368640,737280,1105920,1474560,1843200,2211840,2580480,2949120,3317760,0,737280,1474560,2211840,2949120,3686400}

    Returns: 458889382

  34. {6480,12960,19440,25920,32400,38880,45360,51840,58320,0,9720,19440,29160,38880,48600,58320,68040,77760,87480,0,12960,25920,38880,51840,64800,77760,90720,103680,116640,0,16200,32400}

    Returns: 589921

  35. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4214784,8429568,12644352,16859136,21073920,25288704,29503488,33718272,37933056,0,8429568,16859136,25288704,33718272,42147840,50577408,59006976,67436544,75866112,0,12644352,25288704,37933056,50577408,63221760}

    Returns: 37778888096

  36. {11520,0,1440,2880,4320,5760,7200,8640,10080,11520,12960,0,0,0,0,0,0,0,0,0,0,0,240,480,720,960,1200,1440,1680}

    Returns: 258289

  37. {6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8,12,16,20,24,28,32,36,0}

    Returns: 16

  38. {145152,217728,290304,362880,435456,508032,580608,653184,0,90720,181440,272160,362880,453600,544320,635040,725760,816480,0,108864,217728,326592,435456,544320,653184,762048,870912,979776,0,127008,254016,381024,508032,635040,762048}

    Returns: 4789942

  39. {0,0,0,0,0,0,0,0,0,17781120,35562240,53343360,71124480,88905600,106686720,124467840}

    Returns: 25777889902

  40. {0,0,0,0,0,0,0,0,0,8,16,24,32,40,48,56,64,72,0,16,32,48,64,80}

    Returns: 802

  41. {900,1080,1260,1440,1620,0,270,540,810,1080,1350,1620,1890,2160,2430,0,360,720,1080,1440,1800,2160,2520,2880}

    Returns: 25925

  42. {14171760,0,3149280,6298560,9447840,12597120,15746400,18895680,22044960,25194240,28343520,0,4723920,9447840,14171760,18895680,23619600,28343520,33067440,37791360,42515280,0,6298560,12597120,18895680,25194240,31492800,37791360,44089920,50388480,56687040,0,7873200,15746400,23619600,31492800,39366000,47239200,55112400,62985600,70858800,0,9447840,18895680,28343520,37791360,47239200}

    Returns: 568999919

  43. {248832,497664,746496,995328,1244160,1492992,1741824,1990656,2239488,0,373248,746496,1119744,1492992,1866240,2239488,2612736,2985984,3359232,0,497664,995328,1492992,1990656,2488320,2985984,3483648,3981312,4478976,0,622080,1244160,1866240,2488320,3110400,3732480,4354560,4976640,5598720,0,746496,1492992}

    Returns: 38889921

  44. {0,0,0,0,0,0,0,0,0,6,12,18,24,30,36}

    Returns: 602

  45. {0,0,0,0,2,4,6,8,10,12,14,16,18,0,4,8,12,16,20,24,28,32,36,0,6,12,18,24,30,36,42,48,54,0,8,16,24,32,40,48,56,64,72,0,10}

    Returns: 207

  46. {979776,1143072,1306368,1469664,0,0,0,0,0,0,0,0,0,0,0,20736,41472,62208,82944,103680,124416,145152,165888,186624,0,41472,82944,124416,165888,207360,248832,290304,331776,373248,0,62208,124416,186624,248832,311040}

    Returns: 4899796

  47. {3240,3888,4536,5184,5832,0}

    Returns: 8995

  48. {2857680,3333960,3810240,4286520,0,952560,1905120,2857680,3810240,4762800,5715360,6667920,7620480,8573040,0,1428840,2857680,4286520,5715360,7144200,8573040,10001880,11430720,12859560,0,1905120,3810240,5715360}

    Returns: 357789916

  49. {1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18}

    Returns: 1

  50. {25,30,35,40,45,0,6,12,18,24,30,36,42,48,54,0,7,14,21,28,35,42,49,56,63,0,8,16,24,32,40,48,56,64,72}

    Returns: 55

  51. {0,0,0,0,0,0,0,0,0,0,25515,51030,76545,102060,127575,153090,178605,204120,229635,0}

    Returns: 5799901

  52. {0,0,0,0,0,0,0,288,576,864,1152,1440,1728,2016,2304,2592,0,576,1152,1728,2304,2880,3456,4032}

    Returns: 48904

  53. {0,324,648,972,1296,1620,1944,2268,2592,2916,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 4990

  54. {0,0,0,0,0,0,0,0,0,36,72,108,144,180,216,252,288,324,0,72,144,216,288,360,432,504,576,648,0,108,216,324,432,540,648,756,864,972,0,144,288,432,576,720,864,1008,1152,1296,0}

    Returns: 4902

  55. {240,280,320,360,0,48,96,144,192,240,288,336,384,432,0,56,112,168,224,280,336,392,448,504,0,64,128,192,256,320,384,448,512,576,0,72,144,216,288,360,432,504,576,648,0,0,0,0,0}

    Returns: 856

  56. {144,0,20,40,60,80,100,120,140,160,180,0,24,48,72,96,120,144,168,192,216,0,28,56,84,112,140,168,196,224,252,0,32,64,96,128,160,192,224,256,288,0,36,72,108}

    Returns: 449

  57. {80621568,120932352}

    Returns: 2688899992

  58. {30,35,40,45,0,6,12,18,24,30,36,42,48,54,0,7,14,21,28,35,42}

    Returns: 56

  59. {5443200,7257600,9072000,10886400,12700800,14515200,16329600,0,2721600,5443200,8164800,10886400,13608000,16329600,19051200,21772800,24494400,0}

    Returns: 557889923

  60. {72030,86436,100842}

    Returns: 677775

  61. {1075200,1344000,1612800,1881600,2150400,2419200,0,302400,604800,907200,1209600,1512000,1814400,2116800,2419200,2721600,0,0,0,0}

    Returns: 35578884

  62. {49,56,63,0,8,16,24,32,40,48,56,64,72,0,9,18,27,36,45,54,63,72,81,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,0,2,4,6}

    Returns: 77

  63. {104976,122472,139968,157464,0,23328,46656,69984,93312,116640,139968,163296,186624,209952,0,29160,58320}

    Returns: 899936

  64. {4608,6144,7680,9216,10752,12288,13824}

    Returns: 38883

  65. {24,48,72,96,120,144,168}

    Returns: 381

  66. {1152,1728,2304,2880,3456,4032,4608,5184}

    Returns: 8892

  67. {2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8,12,16,20}

    Returns: 2

  68. {4,5,6,7,8,9,0,1,2,3,4,5}

    Returns: 4

  69. {210,240,270,0,35,70,105,140,175,210,245,280,315,0,40,80,120,160,200,240,280,320,360,0,45}

    Returns: 567

  70. {0,0,0,0,9408,18816,28224,37632,47040,56448,65856,75264,84672,0,18816,37632,56448,75264,94080,112896,131712,150528,169344,0,28224,56448,84672,112896,141120,169344,197568,225792,254016,0,37632,75264,112896,150528,188160,225792,263424,301056,338688,0,47040,94080,141120,188160,235200,282240}

    Returns: 3778807

  71. {6,8,10,12,14,16,18,0,3,6,9,12,15,18}

    Returns: 23

  72. {2041200,4082400,6123600,8164800,10206000,12247200,14288400,16329600,18370800,0,4082400,8164800,12247200,16329600,20412000,24494400,28576800,32659200,36741600,0,6123600,12247200,18370800,24494400,30618000,36741600,42865200,48988800,55112400,0,8164800,16329600,24494400,32659200,40824000,48988800,57153600,65318400,73483200,0,10206000,20412000,30618000,40824000,51030000}

    Returns: 2557899911

  73. {18816,21504,24192,0,5376,10752,16128,21504,26880,32256,37632,43008,48384,0,8064,16128,24192,32256,40320,48384,56448,64512,72576,0,10752,21504,32256,43008}

    Returns: 678817

  74. {350,525,700,875,1050,1225,1400,1575,0,210,420,630,840}

    Returns: 5752

  75. {0,2268,4536,6804,9072,11340,13608,15876,18144,20412,0,3024,6048,9072,12096,15120,18144,21168,24192,27216,0,3780,7560,11340,15120,18900,22680,26460,30240,34020,0,4536,9072,13608,18144,22680,27216}

    Returns: 267930

  76. {4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12}

    Returns: 4

  77. {61236000,81648000,102060000,122472000}

    Returns: 4555789993

  78. {8400,10080,11760,13440,15120,0,1960,3920,5880,7840,9800,11760,13720,15680,17640,0,2240,4480,6720,8960,11200,13440,15680,17920}

    Returns: 57865

  79. {420,490,560,630,0,105,210,315,420,525,630,735,840,945,0,140,280,420,560,700,840,980,1120}

    Returns: 5726

  80. {680244480,765275040,0,99202320}

    Returns: 5689999968

  81. {168,224,280,336,392,448,504,0,112,224,336,448,560,672,784,896,1008,0,168,336,504,672,840,1008,1176,1344,1512,0,224}

    Returns: 7813

  82. {180,270,360,450,540,630,720,810,0,0,0,0,0,0,0,0,0,0,0,15,30,45,60,75,90,105,120,135,0,30,60}

    Returns: 5292

  83. {150,180,210,240,270,0,35,70}

    Returns: 565

  84. {20160,22680,0,5040,10080,15120,20160,25200,30240,35280,40320,45360,0,7560,15120,22680,30240,37800,45360,52920,60480,68040,0,10080,20160,30240,40320,50400,60480,70560,80640,90720,0,12600,25200,37800,50400,63000,75600,88200}

    Returns: 578918

  85. {28449792,32514048,36578304,0,4644864,9289728,13934592,18579456,23224320,27869184,32514048,37158912,41803776,0,5225472,10450944,15676416,20901888,26127360,31352832,36578304,41803776,47029248,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 278889977

  86. {486,0,63,126,189,252,315,378,441,504,567,0,72,144,216,288,360,432,504,576,648,0,81,162,243,324,405,486,567,648,729,0,0,0,0,0,0,0,0,0,0}

    Returns: 969

  87. {0,0,0,0,0,0,0,0,2160,4320,6480,8640,10800,12960,15120,17280,19440,0,4320,8640,12960,17280,21600,25920,30240,34560,38880,0,6480,12960,19440,25920,32400,38880,45360,51840,58320,0,8640,17280,25920,34560,43200,51840,60480}

    Returns: 568903

  88. {20,30,40,50,60,70,80,90,0,15,30,45,60,75,90,105,120,135,0,20,40,60,80}

    Returns: 522

  89. {62705664,83607552,104509440,125411328,146313216,167215104,188116992,0,41803776}

    Returns: 7888899913

  90. {0,0,0,0,0,0,0,0,0,0,40,80,120,160,200,240,280,320,360,0,80,160,240,320,400,480,560,640,720,0,120,240,360,480,600,720,840,960,1080,0,160,320,480,640,800,960,1120}

    Returns: 5801

  91. {0,1990656,3981312,5971968,7962624,9953280,11943936,13934592,15925248,17915904,0,2654208,5308416,7962624,10616832,13271040,15925248,18579456,21233664,23887872,0,3317760,6635520,9953280,13271040,16588800,19906560,23224320}

    Returns: 288889930

  92. {612360,0,77760,155520,233280,311040,388800,466560,544320,622080,699840,0}

    Returns: 3589979

  93. {80,90,0,15,30,45,60,75,90,105,120,135,0,20,40,60,80,100,120,140,160,180,0,25,50,75,100,125,150,175,200,225,0,30,60,90,120,150,180,210,240,270,0,35,70,105}

    Returns: 528

  94. {6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18}

    Returns: 16

  95. {8,16,24,32,40,48,56,64,72,0,9,18,27,36,45,54,63,72,81,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18}

    Returns: 81

  96. {50803200,0,7526400,15052800,22579200,30105600,37632000,45158400,52684800,60211200,67737600,0,9408000,18816000,28224000,37632000,47040000,56448000,65856000,75264000,84672000,0,11289600,22579200,33868800,45158400,56448000,67737600,79027200,90316800,101606400,0,13171200,26342400,39513600,52684800,65856000,79027200,92198400}

    Returns: 3557788839

  97. {8640,11520,14400,17280,20160,23040,25920,0,0,0,0,0,0,0,0,0,0,0,640,1280,1920,2560,3200,3840,4480,5120,5760,0,1280}

    Returns: 588193

  98. {1680,1890,0,240,480,720,960,1200,1440,1680,1920,2160,0,270,540,810,1080,1350,1620,1890,2160,2430,0,0,0,0,0,0,0,0,0,0,0,35,70,105,140,175,210,245,280,315,0,70}

    Returns: 5678

  99. {1058400,2116800,3175200,4233600,5292000,6350400,7408800,8467200,9525600,0,1270080,2540160,3810240,5080320,6350400,7620480,8890560,10160640,11430720,0,1481760,2963520,4445280,5927040,7408800,8890560,10372320,11854080,13335840,0,1693440}

    Returns: 256778951

  100. {41472,48384,55296,62208,0,8064,16128,24192,32256,40320,48384,56448,64512,72576,0,9216,18432,27648,36864,46080,55296,64512,73728,82944,0,10368,20736}

    Returns: 288966

  101. {209952,0,31104,62208,93312,124416,155520,186624,217728,248832,279936,0,38880,77760,116640,155520,194400,233280,272160,311040,349920,0,46656}

    Returns: 2689939

  102. {0,486,972}

    Returns: 6990

  103. {720,1080,1440,1800,2160,2520,2880,3240,0,432,864,1296,1728,2160,2592,3024,3456,3888,0,504,1008,1512,2016,2520,3024,3528,4032,4536,0,576,1152,1728,2304,2880,3456,4032,4608,5184,0}

    Returns: 8952

  104. {5376}

    Returns: 26788

  105. {16796160,20155392,23514624,26873856}

    Returns: 88899995

  106. {23224320,27869184,32514048,37158912,41803776,0,5225472,10450944,15676416,20901888,26127360,31352832,36578304,41803776,47029248,0,0,0,0,0,0,0,0,0,0,0,677376,1354752,2032128,2709504,3386880,4064256,4741632,5419008,6096384}

    Returns: 378889685

  107. {9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8,12,16,20,24,28,32,36,0,5,10,15}

    Returns: 9

  108. {2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8,12,16,20,24,28,32,36}

    Returns: 2

  109. {7,8,9,0,1}

    Returns: 7

  110. {320,384,448,512,576,0,72,144,216,288,360,432,504,576,648,0,0,0,0,0,0,0,0,0,0,0,9,18,27}

    Returns: 885

  111. {20736000,24883200,29030400,33177600,37324800,0,5184000,10368000,15552000,20736000,25920000,31104000,36288000,41472000,46656000,0,6220800,12441600,18662400,24883200,31104000,37324800,43545600,49766400,55987200,0,7257600,14515200,21772800,29030400,36288000,43545600,50803200,58060800,65318400,0,8294400,16588800,24883200,33177600,41472000,49766400,58060800,66355200,74649600,0,9331200}

    Returns: 558889945

  112. {0,0,0,0,0,0,0,0,10,20,30,40,50,60,70,80,90,0,20}

    Returns: 2503

  113. {31104}

    Returns: 68899

  114. {864,972,0,0,0,0,0,0,0,0,0,0,0,24,48,72,96,120,144,168,192,216,0,48,96,144,192,240,288,336,384,432,0,72,144,216,288,360,432,504,576,648,0,96,192,288,384,480,576}

    Returns: 26198

  115. {48771072,60963840,73156608,85349376}

    Returns: 677888994

  116. {162,0,27,54,81,108,135,162,189,216,243,0,36,72}

    Returns: 929

  117. {2268,0,378,756,1134,1512,1890,2268,2646,3024,3402,0,504,1008,1512,2016,2520,3024,3528,4032,4536,0,630,1260,1890,2520,3150,3780}

    Returns: 27929

  118. {1344,1568,1792,2016,0,252,504,756,1008,1260,1512,1764,2016,2268,0,0,0,0,0,0,0,0,0,0,0,32,64,96,128,160,192,224,256,288,0,64,128,192,256,320,384,448,512,576,0,96,192}

    Returns: 4786

  119. {2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10}

    Returns: 2

  120. {1000000000}

    Returns: 555555555888

  121. {1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0,4,8,12,16,20,24,28}

    Returns: 1

  122. {349920}

    Returns: 2568999

  123. {567,648,729,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 997

  124. {729,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 999

  125. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,6,9,12,15,18,21,24,27,0}

    Returns: 1097

  126. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6}

    Returns: 1072

  127. {5806080,7257600,8709120,10160640,11612160,13063680,0,1814400,3628800,5443200,7257600}

    Returns: 257889944

  128. {0,1968300,3936600,5904900,7873200,9841500,11809800,13778100,15746400,17714700,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 255699990

  129. {629856000,0,0,0,0,0,0,0,0,0,0,0}

    Returns: 25556889999

  130. {0,360}

    Returns: 5890

  131. {31104,0,4608,9216,13824,18432,23040,27648,32256,36864,41472,0}

    Returns: 288939

  132. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,160030080,320060160,480090240,640120320,800150400}

    Returns: 2577788999076

  133. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,145152000}

    Returns: 4555788899078

  134. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,316108800}

    Returns: 5577788889067

  135. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1889568}

    Returns: 4899999065

  136. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,108}

    Returns: 269075

  137. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3072}

    Returns: 6888092

  138. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,531441}

    Returns: 999999079

  139. {0,0,0,0,0,0,0,0,0,0,0,0,0,46656}

    Returns: 88999098

  140. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,124416}

    Returns: 388899093

  141. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8192}

    Returns: 28888074

  142. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,128}

    Returns: 288092

  143. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,19131876}

    Returns: 49999999094

  144. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,41472}

    Returns: 88899093

  145. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,136048896}

    Returns: 488999999068

  146. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}

    Returns: 1071

  147. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,331776}

    Returns: 888899078

  148. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2834352}

    Returns: 6899999072

  149. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,509607936}

    Returns: 3888888899066

  150. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,30233088}

    Returns: 88899999067

  151. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,209952}

    Returns: 489999097

  152. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,39366}

    Returns: 69999065

  153. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2359296}

    Returns: 8888889096

  154. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,914457600}

    Returns: 25577888999062

  155. {111132000, 166698000, 222264000, 277830000, 333396000, 388962000, 444528000, 500094000, 0, 64827000, 129654000, 194481000, 259308000, 324135000, 388962000, 453789000, 518616000, 583443000, 0, 74088000, 148176000, 222264000, 296352000, 370440000, 444528000, 518616000, 592704000, 666792000, 0, 83349000, 166698000, 250047000, 333396000, 416745000, 500094000, 583443000, 666792000, 750141000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18522000 }

    Returns: 355577789162

  156. {840, 1260, 1680, 2100, 2520, 2940, 3360, 3780, 0, 480, 960, 1440, 1920, 2400, 2880, 3360, 3840, 4320, 0, 540, 1080, 1620, 2160, 2700, 3240, 3780, 4320, 4860, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 144, 216, 288, 360, 432, 504, 576, 648, 0, 144 }

    Returns: 26572

  157. {81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 }

    Returns: 199

  158. {182891520, 209018880, 235146240, 0, 29393280, 58786560, 88179840, 117573120, 146966400, 176359680, 205752960, 235146240, 264539520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3919104, 7838208, 11757312, 15676416, 19595520, 23514624, 27433728, 31352832, 35271936, 0, 7838208, 15676416, 23514624, 31352832, 39191040, 47029248, 54867456, 62705664, 70543872, 0, 11757312, 23514624, 35271936, 47029248, 58786560, 70543872 }

    Returns: 2788999587

  159. {209018880, 235146240, 0, 34836480, 69672960, 104509440, 139345920, 174182400, 209018880, 243855360, 278691840, 313528320, 0, 43545600, 87091200, 130636800, 174182400, 217728000, 261273600, 304819200, 348364800, 391910400, 0, 52254720, 104509440, 156764160, 209018880, 261273600, 313528320, 365783040, 418037760, 470292480, 0, 60963840, 121927680, 182891520, 243855360, 304819200, 365783040, 426746880, 487710720, 548674560, 0, 69672960, 139345920, 209018880, 278691840, 348364800, 418037760, 487710720 }

    Returns: 5678889938

  160. {685843200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11289600 }

    Returns: 45577889399

  161. {34020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 840, 1680, 2520, 3360, 4200, 5040, 5880, 6720, 7560, 0, 1680, 3360, 5040, 6720, 8400, 10080, 11760, 13440, 15120, 0, 2520, 5040, 7560, 10080, 12600, 15120, 17640, 20160, 22680, 0, 3360, 6720, 10080, 13440, 16800, 20160, 23520, 26880 }

    Returns: 2567199

  162. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 705438720 }

    Returns: 5678889999062

  163. {0 }

    Returns: 10

  164. {244944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6048 }

    Returns: 6789199

  165. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }

    Returns: 1062

  166. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    Returns: 100

  167. {435456000, 870912000 }

    Returns: 255567888991

  168. {344373768, 387420489, 0, 86093442, 172186884, 258280326, 344373768, 430467210, 516560652, 602654094, 688747536, 774840978, 0, 129140163, 258280326, 387420489 }

    Returns: 9999999918

  169. {5443200, 10886400, 16329600, 21772800, 27216000, 32659200, 38102400, 43545600, 48988800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 907200, 1814400, 2721600, 3628800, 4536000, 5443200, 6350400, 7257600, 8164800, 0, 1814400, 3628800, 5443200, 7257600, 9072000, 10886400, 12700800, 14515200, 16329600, 0, 2721600, 5443200, 8164800, 10886400, 13608000, 16329600, 19051200, 21772800, 24494400, 0 }

    Returns: 3557889291

  170. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }

    Returns: 1071

  171. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 }

    Returns: 4062

  172. {81000000, 0, 10125000, 20250000, 30375000, 40500000, 50625000, 60750000, 70875000, 81000000, 91125000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1265625, 2531250, 3796875, 5062500, 6328125, 7593750, 8859375, 10125000, 11390625, 0, 2531250, 5062500, 7593750, 10125000, 12656250, 15187500, 17718750, 20250000, 22781250, 0, 3796875, 7593750, 11390625, 15187500, 18984375, 22781250, 26578125, 30375000 }

    Returns: 5555559889

  173. {0, 4032, 8064, 12096, 16128, 20160, 24192, 28224, 32256, 36288, 0, 4536, 9072, 13608, 18144, 22680, 27216, 31752, 36288, 40824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1008, 2016, 3024, 4032, 5040, 6048, 7056, 8064, 9072, 0, 2016, 4032, 6048, 8064, 10080, 12096, 14112, 16128, 18144 }

    Returns: 789180

  174. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 114307200, 228614400, 342921600, 457228800, 571536000, 685843200, 800150400, 914457600 }

    Returns: 2557788999069

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