Statistics

Problem Statement for "FactorialTower"

Problem Statement

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Given an int m and a int[] a containing n numbers, return the result of the following expression:

Definition

Class:
FactorialTower
Method:
exprValue
Parameters:
int[], int
Returns:
int
Method signature:
int exprValue(int[] a, int m)
(be sure your method is public)

Notes

  • The expression is calculated from top to bottom. See example 5.
  • "x mod y" means the remainder of x divided by y.
  • Assume 0! = 1.

Constraints

  • a will contain between 1 and 50 elements, inclusive.
  • Each element of a will be between 0 and 2147483647, inclusive.
  • m will be between 1 and 40000, inclusive.

Examples

  1. {2,2,2,2}

    10

    Returns: 6

    Last digit of 65536.

  2. {3,8}

    100

    Returns: 76

    (3!8!) mod 100 = 76.

  3. {775,967,1,1,1}

    39877

    Returns: 4832

  4. {0}

    40000

    Returns: 1

    Remember that 0! is 1.

  5. {5,4,123456789,987654321,687955994,1162330089,195458992,1687386387, 1092101949,1086091397,902287014,341660341,1600834655,131565486,1494304912, 384585199,1883009662,916903507,1895924341,397197724,1883021244,1616061080, 1437763283,621297237,1883141487,282508826,285957625,1249530903,1484124572, 1822993209,1668351723,174237628,1589170712,992959839,1281777023,1158939002, 1488964134,1806511164,1519656093,159671689,542573000,1571768398,1203500608, 1053387535,793607740,1535801392,1798307613,552983945,901802936,1023595016}

    40000

    Returns: 0

  6. {3,0}

    5

    Returns: 1

  7. {39,1}

    1353

    Returns: 165

  8. {39,0}

    1353

    Returns: 165

  9. {39}

    1353

    Returns: 165

  10. {2,2}

    36864

    Returns: 4

  11. {2,2,2}

    36864

    Returns: 16

  12. {2,3}

    36864

    Returns: 64

  13. {2,3,2}

    36864

    Returns: 4096

    The expression is calculated from top to bottom. (2! to the power of (3!2!)) mod 36864 = 4096.

  14. {2,0}

    36864

    Returns: 2

  15. {2,1}

    160

    Returns: 2

  16. {2,2}

    160

    Returns: 4

  17. {2,3}

    160

    Returns: 64

  18. {2,4}

    160

    Returns: 96

  19. {2,5}

    160

    Returns: 96

  20. {39595,10513,123,32,2,2,0}

    39983

    Returns: 18526

  21. {39595,10513,123,32,2,2,2}

    39983

    Returns: 9411

  22. {2,2,2,2}

    36864

    Returns: 28672

  23. {6,568,0}

    10000

    Returns: 0

  24. {5,999,2150000}

    25

    Returns: 0

  25. {319,846,215,7467}

    1

    Returns: 0

  26. {1,7,199}

    39991

    Returns: 1

  27. {30000}

    39301

    Returns: 13487

  28. {3,7,6,2}

    100

    Returns: 76

  29. {8,1,999999999}

    2

    Returns: 0

  30. {1,0}

    1

    Returns: 0

  31. {0}

    1

    Returns: 0

  32. {0}

    2

    Returns: 1

  33. {0}

    40000

    Returns: 1

  34. {1}

    10

    Returns: 1

  35. {0,1}

    39991

    Returns: 1

  36. {6,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647,2147483647}

    39953

    Returns: 1

  37. {39988}

    39989

    Returns: 39988

  38. {15150}

    39989

    Returns: 21709

  39. {15150,0}

    39989

    Returns: 21709

  40. {15150,2}

    39989

    Returns: 10316

  41. {15150,7}

    39989

    Returns: 33422

  42. {15150,15150}

    39989

    Returns: 1

  43. {15150,908573485,123456789,987654321,687955994,1162330089,195458992,1687386387,1092101949,1086091397,902287014,341660341,1600834655,131565486,1494304912,384585199,1883009662,916903507,1895924341,397197724,1883021244,1616061080,1437763283,621297237,1883141487,282508826,285957625,1249530903,1484124572,1822993209,1668351723,174237628,1589170712,992959839,1281777023,1158939002,1488964134,1806511164,1519656093,159671689,542573000,1571768398,1203500608,1053387535,793607740,1535801392,1798307613,552983945,901802936,1023595016}

    39989

    Returns: 1

  44. {5,4,123456789,987654321,687955994,1162330089,195458992,1687386387,1092101949,1086091397,902287014,341660341,1600834655,131565486,1494304912,384585199,1883009662,916903507,1895924341,397197724,1883021244,1616061080,1437763283,621297237,1883141487,282508826,285957625,1249530903,1484124572,1822993209,1668351723,174237628,1589170712,992959839,1281777023,1158939002,1488964134,1806511164,1519656093,159671689,542573000,1571768398,1203500608,1053387535,793607740,1535801392,1798307613,552983945,901802936,1023595016}

    40000

    Returns: 0

  45. {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}

    40000

    Returns: 1

  46. {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}

    2

    Returns: 1

  47. {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}

    1

    Returns: 0

  48. {1,1,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    40000

    Returns: 1

  49. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    40000

    Returns: 1

  50. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    2

    Returns: 1

  51. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    1

    Returns: 0

  52. {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}

    36864

    Returns: 28672

  53. {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}

    2

    Returns: 0

  54. {1,1,1,1,1,1,1,1,1,1,1,1,39595,10513,123,32,2,2,2,1,1,1,1,1,1}

    39983

    Returns: 1

  55. {39595,10513,123,32,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    39983

    Returns: 9411

  56. {39595,10513,123,32,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 9411

  57. {39595,10513,123,32,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,39595,10513,123,32,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    39983

    Returns: 9411

  58. {2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1}

    28677

    Returns: 2

  59. {39595,10513,31,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 32260

  60. {39595,10513,31,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 23029

  61. {39595,10513,31,4,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 16500

  62. {39595,10513,31,4,5,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 18526

  63. {39595,10513,31,4,5,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 18526

  64. {39595,10513,31,4,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 18526

  65. {39595,10513,31,4,28,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 18526

  66. {39595,10513,31,4,28,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 18526

  67. {39595,10513,31,4,28,687955994,1162330089,195458992,1687386387,1092101949,1086091397,902287014,341660341,1600834655,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    39983

    Returns: 18526

  68. {3,1}

    5

    Returns: 1

  69. {2,17}

    39989

    Returns: 29110

  70. {2,15}

    32768

    Returns: 0

  71. {2,16}

    32768

    Returns: 0

  72. {2,14}

    32768

    Returns: 0

  73. {3,5330}

    32768

    Returns: 0

  74. {3,40000}

    32768

    Returns: 0

  75. {3,39999}

    32768

    Returns: 0

  76. {3,29999}

    32768

    Returns: 0

  77. {3,19999}

    32768

    Returns: 0

  78. {3,9999}

    32768

    Returns: 0

  79. {2,1,500,600}

    34816

    Returns: 2

  80. {2,500,600}

    34816

    Returns: 30720

  81. {2, 3, 2, 1, 10, 10, 3, 4, 7, 1, 4, 10, 9}

    97

    Returns: 75

  82. {7, 3, 2, 1, 10, 8, 10, 2, 3, 8, 2, 3, 1, 7, 3, 2, 1, 4, 5, 7, 8, 5, 3, 7, 3, 8, 8, 6, 1, 8, 1, 6, 3, 5, 6, 4, 5, 1, 3, 8, 6, 9, 7, 3, 6, 4, 2, 10, 5}

    82

    Returns: 40

  83. {9, 2, 2, 1}

    233

    Returns: 225

  84. {9, 2, 2}

    233

    Returns: 225

  85. {4, 3, 2, 1, 3, 8, 4, 6, 10, 4, 8, 9, 7, 4, 3, 2, 7, 3, 7, 5}

    578

    Returns: 310

  86. {2, 2, 1, 10, 10, 2, 6}

    536

    Returns: 4

  87. {5, 3, 2, 1}

    723

    Returns: 240

  88. {3, 2, 1, 5}

    392

    Returns: 36

  89. {2, 2, 0, 7, 5, 3, 2, 9, 9, 0, 8, 7, 10}

    72

    Returns: 4

  90. {2, 2, 0, 7, 5, 3, 2, 9, 9, 0, 8, 7, 10}

    20

    Returns: 4

  91. {2, 2, 0, 7}

    15

    Returns: 4

  92. {2, 2, 0, 7 }

    20

    Returns: 4

  93. {2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647 }

    40000

    Returns: 0

  94. {0 }

    1

    Returns: 0

  95. {3, 2, 5, 7 }

    40000

    Returns: 16256

  96. {2, 2 }

    128

    Returns: 4

  97. {2, 0 }

    4

    Returns: 2

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