Statistics

Problem Statement for "Permutant"

Problem Statement

Hero likes combinatorics. He is especially fond of complicated formulas related to permutations. Hero has a int[] a containing n (not necessarily distinct) positive integers. The sum of these integers is m.

There are n! permutations of the array a. For each of these permutations, Hero does the following computation:

  1. Let b be the permuted array a.
  2. Let s be the array of prefix sums of the array b. That is, for each i, s[i] is the sum of the first i elements of b.
  3. Hero computes the value m! / (s[2] * s[3] * ... * s[n]). Note that the product in the denominator starts with s[2], not s[1].

For example, suppose that b = {3,1,2}. This means that m = 3+1+2 = 6. The relevant prefix sums are s[2] = 3+1 = 4 and s[3] = 3+1+2 = 6. The value Hero computes is 6! / (4 * 6) = 30.

At the end, Hero will have n! values (one for each possible permutation of a). Let X be the sum of all those values. Help him by computing and returning the value (X modulo 1,000,000,007).

Definition

Class:
Permutant
Method:
counthis
Parameters:
int[]
Returns:
int
Method signature:
int counthis(int[] a)
(be sure your method is public)

Notes

  • It can easily be shown that each of the n! values computed by Hero is a positive integer.

Constraints

  • Number of elements in a will be between 1 and 50, inclusive.
  • Each element in a will be between 1 and 50, inclusive.
  • Sum of elements in a will be between 1 and 1000, inclusive.

Examples

  1. {1,1}

    Returns: 2

    For the given a we have n = 2 and m = 1+1 = 2. There are n! = 2 permutations of a. For each of them, we have b = {1,1}, s[2] = 2, and thus Hero computes the value 2! / 2 = 1. The sum of all computed values is X = 1 + 1 = 2.

  2. {1,2}

    Returns: 4

  3. {1,2,3}

    Returns: 188

    The six permutations of a give us the following six values computed by Hero: 24, 24, 30, 30, 40, and 40.

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

    Returns: 120

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

    Returns: 860993751

  6. {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    Returns: 207899433

  7. {20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20}

    Returns: 203841389

  8. {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,20,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: 822611828

  9. {19,37,38,5,48,14,36,1,13,4,1,41,31,37,21,46,36,48,28,26,42,5,7,7,23,31,40,25,28,47,40,39,38,7,38,12,18,5,18}

    Returns: 831285810

  10. {43,48,26,22,5,24,3,20,5,40,37}

    Returns: 274103809

  11. {38,24,36,34,44}

    Returns: 930191442

  12. {25,34,12,25,16,20,31,18,37,50,37,20,28,1,24,23,25,12,13,16,42}

    Returns: 850710413

  13. {48,1,21,35,19,25,28,47,32,9,23,31,35,32,36,18,11,15,43,27}

    Returns: 516988323

  14. {24,45,19,45,25,22,8,47,27,14,41,13,48,31,48,29,14,34,10,44,42,45,12,34,23,2,5,21}

    Returns: 633800659

  15. {25,22,23,11,3,49,7,12,26,37,20,39,6,48,41,5,44,6,42,5}

    Returns: 522496418

  16. {17,7,2,28,15,2,34,30,25,47,15,50,16,38,11,3,26,11}

    Returns: 110354324

  17. {1,23,34,6,8,19,48,26,42,41,28,44,32,17,23,48,13,42,24,33,46,16,7,26,30,28,34,4,48,33,13,2,45,7,46,42,10}

    Returns: 117996452

  18. {14,45,5,16,19,28,34,39,45,9,6,27,48,35,28}

    Returns: 865032499

  19. {26,31,3,23,46,17,12,8,40,10,11,26,41,15,27,44,48,16,40,43,11}

    Returns: 648558244

  20. {47,12,30,29,5,9,49,37,4,9,44,24,34,4,27,10,41,26,3,29,2,5,35,3,5,36,3,5,33,49,38,2}

    Returns: 916922307

  21. {27,18,33,24,33,16,39,27,4,44,29,39,30,18,28,45}

    Returns: 809085561

  22. {3,8,12,11,20,7,11,44,8,13,44,27,36,13,6,15,41,27,14,37,11,2,31}

    Returns: 847462081

  23. {3,36,22,2,9,43,41,10,20,31,19,49,2,35,37,28,22,4,21,2,50,23,3,15,32,37,30,12,12,38,40,50,46,38,2,14,16,50}

    Returns: 120460148

  24. {35,30,44,38,2,43,17,39,42,15,43,9,1,35,4,42,2}

    Returns: 271207574

  25. {2,33,10,42,9,14,24,3,36,6,45,17,1,43,5,5,43,33,40,6,29,43,9,3,11,47,43,42,46,1,49,10,24,46,10,47,23,30,9,26,23,12}

    Returns: 395613186

  26. {3,21,5,34,37,15,33,46,33,29,25,43,1,45,1,21,4,29,27,13,18,42,46,22,22,16,46,11,18,25,3,21,19,7,25,46,6,1,46,45,12,38}

    Returns: 351779290

  27. {32,37,18,33,32,12,8}

    Returns: 403828601

  28. {3,14,32,17,45,44,11,19,28,41,33,42,14,46,8}

    Returns: 512362875

  29. {22,34,34,42,9,6,37,29,37,22,30,7,11,45,39,10,42,48,31,9,8,43}

    Returns: 972024794

  30. {41,13,5,16,12,3,21,34,30,41,18,43,20,36,42,5,24,16,6,27,3,14,30,5,13,30,23,40,43,43,32,24,40,4,24,14,1,13,2,1,23,1,18,4,4,24,4,10,36,24}

    Returns: 326087446

  31. {23,3,22,41,46,43,15,29,15,40,21,11,12,44,15,21,8,32,49,9,3,21,8,12,17,5,8,16,17,15,33,8,14,44,20,13,11,24,35,12,42,3,17,33,23,22,25}

    Returns: 387856888

  32. {17,24,24,32,31,24,19,31,45,15,33,5,24,32,7,43}

    Returns: 250797586

  33. {36,34,37,47,1,42,33,23,5,32,29,41,29,42,2,50,36,50,49,22,2,17,4,44,2,45,44,30,4,1,19,2,50,29,12,27}

    Returns: 791800732

  34. {37,13,3,30,20,25,44,9,12,20,31,30,1,35,21,25,9,3,20,46,40,7,10,33,16,8,47,48,5,29,22,1,8}

    Returns: 723300896

  35. {32,42,8,19,32,37,10,12,36,1,26,8,18,12,25,10,1,22,36,10,16,24,37,34,16,17,10,1,17,19,6,31,42,37,7,44,2,1,23,20,9,23,20,20,42,24,14,21,26}

    Returns: 362387360

  36. {7,24,12,26,36}

    Returns: 248224193

  37. {45,42,3,41,24,6,39,25,16,8,19,26,28,17,40,38,27,28,22,20,42,15,35,20,1,1,9,7,31,32,26,23,42,27,12,2,28,13,39,28,9,1,43}

    Returns: 863256865

  38. {45,14,34,39,27,34,17,31,13,38,5,31,1,6,37,23,24,26,8,7,35,48,6,3,47,8}

    Returns: 520589088

  39. {15,21,3,8,10,5,11,43,33,9,5,46,23,39,25,7,37,48,46,28,46,16,38,28,18,30}

    Returns: 567512157

  40. {1,2,36,25,17,36,8,49}

    Returns: 608560793

  41. {32,43,1,27,17,43,17,25,16,45,3,47,32,32,29,1,10,34,13,16,31,18,49,24,42,28,35,14,38,4,2,14,8,16,24,2,4,1,44,30,35,45,9}

    Returns: 313198913

  42. {25,48,47,27,34,7,6,43,15,5,44,26,2}

    Returns: 620060533

  43. {27,26,20,1,5,8,36,26,43}

    Returns: 597358611

  44. {49,41,10,9,41,1,13,2,24,20,32,43,40,13,37,1,49,29,22,1,34,16,20}

    Returns: 558852475

  45. {9,27,8,20,22,13,40,37,20,32,43,34,29,10,4,50,28,40,2,5,36,14,32,7,22,10,29,1,7,37,13,33,45,20,47,35}

    Returns: 211324463

  46. {25,17,15,48,11,11,32,37,46,12,14,32,33,10,24,37,21,1,19,4,19,33,47,27,5,7,31,27,22,10,46,36,34,9}

    Returns: 472346113

  47. {23,46,13,41,49,2,15,15,8,2,12,41,38,7,9,36,42,38,38,40,39,38,47,1,3,22,23,37,22,21,10,31,48,6}

    Returns: 806041289

  48. {20,25,5,32,8,41,21,36,33,42,18,8,14,43,20,16,17,36,2,39,37,12}

    Returns: 180256225

  49. {13,47,40,20,12,31,36,25,14,5,37,27,15,44,44,29,27,21,35,23,16,30,27,14}

    Returns: 545909132

  50. {40,1,10,44,42,20,11,10,7,38,43,46,1,44,29,14,1,21,9,2,40,4,6,49,24,13,47,39,5,40,31,46,31,25,45,8,23,28,24,16,6,17}

    Returns: 476408029

  51. {12,44,24,6,26,10,39,4,26,38,48,1,12,18,48,30,15}

    Returns: 985568781

  52. {17,30,1,19,32,29,18,17,5,49,28,27,40,42,4,20,49,31,38,11,45,11,8,7,39,35,38,17}

    Returns: 111721512

  53. {14,8,21,5,47,20,24,49,6,23,11,28,8,31,42,24,9,2,37,18,22,48,22,37,20,28,4,6,47,37,32,31,47,30,4,7,13}

    Returns: 284813766

  54. {6,19,27,30,34,1,31,32,17,26,35,45,41}

    Returns: 740589890

  55. {27,30,30,34,11,15,32,49,46,22,31,31}

    Returns: 495550429

  56. {8,47,32,8,14,43,15,30,18,25,35,40,15,32,35,30,27,18,34,26,42,22,48,13,31,15,37,6,13,19,30,21}

    Returns: 736292961

  57. {2,15,26,19,33,2,16,16,8,17,25,27,32,42,14,2,4,14,42,4,23,12,28,20,44,36,30,33,23,10}

    Returns: 803470386

  58. {18,23,45,4,25,25,1,26,48,10,36,34,14,6,35,8,24,24,36,41,6,10,18,42,5,17,1,40,4,2,40,19,34,37,17,22,14,25,26,36,13,46,43}

    Returns: 555705516

  59. {46,37,41,25,10,40,32,35,13,21,42,35,50,40,42,7,34,3,25,30,27,27}

    Returns: 146931147

  60. {40,28,30,22,11,1,31,8,9,1,7,41,14,31,1,32,10,8,18,12,30,1,1,31,35,42,7,16,36,1,33,24,19,17,38,22,35,39,20,44,19,24,22,14,22,1,41,11}

    Returns: 519515361

  61. {18,5,9,36,25,6,11,38,46,30,35,12,48,5,2,31,23,41,20,36,40,34,30,47,20,12,34,47,27,12,35,6,5,34,5,10,2,41,35,46}

    Returns: 804752881

  62. {50,8,45,21,1,16,40,3,16,50,35,24,45,31,39,9,26,21,28,39,38,19,37,33,39,38,20,37}

    Returns: 437610026

  63. {23,6,33,3,37,1,31,50,5,20,4,40,5,15,13}

    Returns: 761407436

  64. {48,44,19,11,16,4,1,26,24,34,44,5,43,5,5}

    Returns: 684724718

  65. {32,21,46,5,41,1,24,7,18,50,49,8,47,33,37,1,37,43,48,23,14,33,50,26,50,21,40,34,3,47,23,8,14,48}

    Returns: 998605193

  66. {4,34,37,35,37,39,8,12,20,13,36,31,23,1,35,13,1,8,21,20,15,1,9,28,39,37,38,11,32,1,1,40,28,5,1,43,44,46,6,31,20,27,27,4,36,2}

    Returns: 489189564

  67. {35,2,36,38,43,34,1,16,17,27,24,8,44,20,50,43,37,26}

    Returns: 364469597

  68. {13,1,3,29,7,36,40,11,2,1,39,39,26,26,19,41,27,39,41,41,9,35,49,32,4,2,40,16,38,36,17,40,42,50,24,41,44}

    Returns: 876666518

  69. {4,26,27,15,46,20,28,43,41,1,12,35,34,6,19,22,20,27,33,43,19,26,43,24,43,31}

    Returns: 563627274

  70. {17,46,12,35,37,12,11,15,15,10,18,10,42,25,7}

    Returns: 847845544

  71. {10,17,30,7,18,50,27,30,3,12,32}

    Returns: 585403772

  72. {39,11,33,21,23,30,5,22,41,33,12,41,46,5}

    Returns: 299650622

  73. {4,21,38,9,12,28,43,26,15,1,8,25,13,39,47,48,6,34,20,39,19,23,35,1,4,45,18,42,46,35,6,11,40,30,28,20,22,20,20,29,30}

    Returns: 458038780

  74. {9,1,30,15,28,9,1,16,13,44,32,14,42,2,5,16,50,4,13,46,49,7,47,6,45,1,1,41,33,39,20,12,26,5}

    Returns: 174493150

  75. {1,18,19,7,34,1,13,30,1,23,29,30,23,22,40,11,1,43,21,5,3,34,30,9,47,3,23,1,28,34,25,1,10,29,4,39,34,41,38,21,36,7,32,34,7,19,37,1,1}

    Returns: 475420175

  76. {19,35,35,6,27,35,21,20,40,41,25,2,32,32,3,13,45,21,43,44,2,17,5}

    Returns: 473633912

  77. {18}

    Returns: 660911389

  78. {13,24,2,5,7,33,5,43,8,11,18,35,36,6,5,26,27,22,44,21,16,18,20,16,33,4,28,29,31}

    Returns: 477077244

  79. {35,1,28,26,47,41,22,22,19,11,16,7,35,41,17,35,45,42,32,5,36,32,11,38,37,30}

    Returns: 49489822

  80. {42,39,5,24,42,35,21,46,30,8,10,20,4,41,43,47,47,12,48,41,38,25,21,44,35,2,6,39,33,50}

    Returns: 339587491

  81. {41,43}

    Returns: 343628543

  82. {2,31,27,27,12,14,32,13,47,16,28,21,28,45,35}

    Returns: 873993244

  83. {27,32,42,44,16,17,17,1,21,6,32,29,39,1,3,1,16,34,24,34,44,5,28,23,28,32,35,2,16,12,17,22,29,17,26,40,17,1,1,33,15,15,8,4,41,38,15}

    Returns: 591882736

  84. {1,31,29,7,27,19,42,49,44,12,7,6,1,32,12,39,22,10,23,50,34,45,41,33,43,10,21,14,22,40,9,27,25,42,1,7,29,27,18}

    Returns: 239201436

  85. {36,34,2,11,38,7,19,39,39,15,18,2,28,39,2,29,16,33,25,37,34,1,22,15,31,7,30,29,13,38,1,24,1,24,21,8,1,1,10,42,1,39,22,23,24,23,33,13}

    Returns: 172189481

  86. {1,45,50,40,2,29,16,48,19,47,41,47,11,2,2,16,37,23,41,47,2,26,50,35,47,39,4,15,16,39}

    Returns: 191654215

  87. {30,45,31,36,48,47,20,28,21,25,25,16,4,13,46,27,3,21,4}

    Returns: 716298337

  88. {4,20,15,28,3,47,6,46,2,32,50,10,38,46}

    Returns: 996760720

  89. {33,36,29,35,3,4,8,10,18,39,34,24,28,33,33,27,25,1,20,17,36,19,27,4,1,18,31,42,25,31,12,1,23,18,6,19,1,1,36,44,1,20,18,12,17,19,25,34,1,1}

    Returns: 273082238

  90. {2,19,12,2,41,31,45,6,11,21,21,48,41,48,24,17,41,10,25,16,24,32,39,21,28,41,15,32,33,14,14,6,13,34,35,47,10,20,42,19}

    Returns: 503039573

  91. {21,50,35,17,32,15,34,48,37,9,23,26,48,33,28,21,15,34,35,6,29,40,31,43}

    Returns: 109134374

  92. {8,22,47,13,50,20,32,49,23,47,13,43,2,41,26,7,8,29,2}

    Returns: 196725539

  93. {27,15,10,7,19,23,13,23,11,17,38,49,49,3,32,8,38,39,47,22,34,39,18,44,35,8,45,39,28,7,50,18,48,37}

    Returns: 440240026

  94. {10,27,14,10}

    Returns: 249419009

  95. {45,48,20,3,8,26,2,2,23,15,3,44,42,2,4,4,15,15,41,19,10,50,36,47,9,1,29,34,6,37,34,31,25,10}

    Returns: 415507737

  96. {6,45,44,7,47,46,48,35,31,27,1,47,13,37,32}

    Returns: 256032584

  97. {16,29,19,30,40,45,22,45,27,20,30,41,40,39,13,15,10,7,20,2,27,6,3,44,26,26,33,1,29,14,46}

    Returns: 800976346

  98. {40,6,30,35,50,18,12,28,21,12,12,4,1,30,46,47}

    Returns: 713518705

  99. {2,27,35,1,38,39,30,5,49,37,39}

    Returns: 514209258

  100. {38,42,22,47,13,13,32,33,24,21,1,1,10,10,7,25,18,38,12,46,33,15,3,42,8,22,21,12,18,14,38,24,27,8,1,40,4,30,3,25,8,47,17,44,43}

    Returns: 312907190

  101. {36,37,33,28,48,46,1,10,4,8}

    Returns: 890922035

  102. {5,1,30,12,31,43,21,4,8,8,14,18,16,41,50,7,24,1,16,16,22,50,49,37,25,11,46,32}

    Returns: 318289913

  103. {7,31,32,1,39,8,13,17,14,12,37,50,1,19,30,17,44,24,28,43,16,11,14,18,31,49,21,12,26,2}

    Returns: 729081649

  104. {28,1,15,16,2,9,33,44,9,18,48,24,23,37}

    Returns: 3544863

  105. {48,26,30,7,32,6,26,32,5,21,3,25,36,11,14,46,22,34,21,6,47,3,4,8,8,38,1,22}

    Returns: 868901006

  106. {33,36,33,29,15,37,16,41,22,25,25,26,35,42,12,10,16,31,19,11,12,17,45,2,10,34,8,37,16,50,37,48,4,39,39,24,4,12,10,4}

    Returns: 173212830

  107. {38,9,22,34,43,15,1,27,37,20,29,43,9,8,35,5,13,16,24}

    Returns: 390813603

  108. {4,20,14,24,39,36,27}

    Returns: 818091494

  109. {34,36,48,21,19,33,17,18,20,31,8,2,10,2,20,35,23,50,31,40,27,6,24,37,36,22,44,45,36,11,50,19,5}

    Returns: 480949532

  110. {45,21,18,28,46}

    Returns: 961486712

  111. {25,31,30,9,32,44,21}

    Returns: 492091212

  112. {50,28,17,43,43,25,3,34,9,33,39,37,44,20,41,14,29,27,15,23,6,23,38,37,11,42,22,2,38,34,17,48,7}

    Returns: 666478255

  113. {33,3,3,27,6,7,19,18,14,2,35,28,32}

    Returns: 351190487

  114. {11,23,34,34,24,33,37,24,22,33,20,14,33,47,50,36,8,10,13,24,49,42,4,13,18,34,25,43,49,40,15,15,47,23,43}

    Returns: 122997234

  115. {38,17,44,33,18,15,41,29,43,33,27,23,41,20,4,41,12,37,47,10,10,8,45,38}

    Returns: 284719986

  116. {13,42,31,26,7,21,43,16,34,1,41,3,15,38,12,36,1,15,25,42,11,39,21,6,5,25,1,30,32,29,17,40,33,43,25,27,42,29,23,10,31,15,4}

    Returns: 91479616

  117. {33,11,30,29,35,30,25,7,45,1,8,28,5,25,37,32,45,22,45,47,1,22,24,31,32,7,9,39,36,10,1,1,10,25,40,6,42,24,27,12,17,44}

    Returns: 133623508

  118. {24,11}

    Returns: 886544603

  119. {20,37,13,2,47,17,34,16,32}

    Returns: 19793616

  120. {23,43,7,34,22,19,34,32,39,13,32,40,1,21,14,25,24,43,34,43,5,1,41,25,17,24,27,8,21,1,47,41,1,16,32,17,21,1,12,14,1,13,2,26,1,42}

    Returns: 641120477

  121. {12,20,44,28,16,41,43,20,15,31,43,20,7,49,13,34,43,32,46,16,22,22,26,19,44,2,10,6,45}

    Returns: 782388291

  122. {1,15,21,36,6,23,37,41,10,45,17,34,38,24,2,23,32,41,19,16,44,19,4,22}

    Returns: 274211723

  123. {27,48,38,20,19,7,13,37,48,42,16,11,41,6,8,44}

    Returns: 376087578

  124. {43,21,7,21,25,41,3,3,30,26,35,4,18,14,25,13,25,10,2,34,29,42,36,42,36,21,2,7,5,8,26,19,26,9,21,1,43,20,20,26,21,28,41,1,14,37,16,3}

    Returns: 701864915

  125. {19}

    Returns: 557316307

  126. {32,14,25,19,17,24,29,3,12,16,31,32,23,22,27,16,16,31,12,14,24,21,41,1,17,42,5,32,44,34,41,50,10,46,38,2,34,39,34,24,6}

    Returns: 62826022

  127. {5,13,34,7,42,13,19,31,37,28,7,10,28,1,48,26,34,42,36,4,41,33,45,42,48}

    Returns: 498265824

  128. {8,33,21,28,28,28,10,38,42,8,7,37,40,10,40,47,12}

    Returns: 602437655

  129. {30,3,30,49,38,6,14}

    Returns: 898057328

  130. {23,44,26,33,42}

    Returns: 92190382

  131. {11,37,28,38,14,21,41,1,12,32,1,15,16,8,13,1,37,15,3,25,45,22,41,46,17,6,8,31,17,32,20,21,6,38,47,25,25,42,43,38,31,8,5,3,14}

    Returns: 872084087

  132. {43,5,46,9,19,7,49,15,24,19,48,13,32,12,41,19}

    Returns: 854454613

  133. {25,23,37,4,34,41,47,49,12,6,25}

    Returns: 695932906

  134. {29,1,9,48,1,7,27,41,23,2,44,49,28,27,2,23,38,27,47,27,18,26,25,24,8,35,20,46}

    Returns: 839567240

  135. {28,32,44,7,49,1,21,46,14,28,2,47,13,46,46,41,1,12,14,2,10,19,17,1}

    Returns: 920219504

  136. {26,28,49,29,17,18,16,2,2,18,18,5,11,45,36,44,27,25,47,6,12,32,36,18,25}

    Returns: 550522703

  137. {36,26,10,5,40,34,11,39,48,7,36,34,47,44,10,29,50,19,50,48,14,44,40,30}

    Returns: 953328823

  138. {38,25,29,11,25,35,32,42,16,32,1,37,43,29,22,23,32,9,24,45,40,19,21,12,38,34,1,16,27,7,45,23,17,22,26,45,23,20,14}

    Returns: 311578261

  139. {28,14,32,4,14,39}

    Returns: 134373207

  140. {23,2,48,32,3,21}

    Returns: 321206190

  141. {31,8,9,2,29,34,1,25,5,38,40,44,24,11,36}

    Returns: 319867166

  142. {16,15,16,5,30,19,36,26,34,9,2,34,49,12}

    Returns: 699332506

  143. {40,16,26,27,46,28,36,27,37,39,50,42,28,11,41,1,41,23,33,46,29}

    Returns: 909748563

  144. {5,20,33,26,11,30,31,36,40}

    Returns: 928195741

  145. {26,3,45,8,39,10,34,42,33,41,32,9,43,32,38,38,15,20,28,50,27,46,26,43,10,26,32,43}

    Returns: 597795897

  146. {12,30,6,35,43,10,4,1,38,28,41,15,1,37,5,9,38,31,37,26,43,31,39,30,19,1,36,12,7,14,18,22,1,1,20,25,18,17,17,24,32,7,31,27,13,19,29}

    Returns: 355721918

  147. {12,25,42}

    Returns: 405091378

  148. {15,25,36,28,2,15,1,7,2,5,30,39,7}

    Returns: 59289319

  149. {8,34,45,40,8,23,1,28,26,21,42,20,3,46,37,16,3,5,8,39,13,16,30,44,21,23,20,37,20,25,11,15,23,33}

    Returns: 613619899

  150. {27,11,28,10,47,17,34,28,42,33,27,28,27}

    Returns: 7731520

  151. {3,20,11,39,11,7,9,25,38,45,33,21,28,9,3,17,32,18,33,6,33,12,36,1,36,42,24,6,43,3,11,6,7,14,3,23,21,4,22,29,47,9,19,18,1,4,12,46,26,34}

    Returns: 238821356

  152. {12,26,11,35,36,6,30,9,35,34,15,32,15,3,37,27,30,29,41,45}

    Returns: 256151215

  153. {1,2,29,37,9,8,1,14,43,6,28,35,44,21,8,36,37,20,7,11,32,9,23,29,19,46,9,7,43,12,18,6,18,14,5,16,19,45,1,11,31,43,20,34,34,19,1,1,27,11}

    Returns: 664418154

  154. {15,9,39,26,27,22,8,32,47,7}

    Returns: 240601161

  155. {2,21,9,44,12,13,22,35,14,9,6,39,30,3,37,34,38}

    Returns: 411119105

  156. {33,1,43,28,20,30,7,31,26,29,16,34}

    Returns: 547105379

  157. {6,16,4,27,46,49,45,11,1,33,40,23,30,17,38,15,26,8,31,37,2,2,10,49,33,12,24,28,31,12,15,11,20}

    Returns: 660743771

  158. {20,24,28,39,14,29,41,16,41,13,40,32,12,7,49,40,42}

    Returns: 400448048

  159. {36,16,15,18,40,28,45,39,47,39,4,25,28,43,10,23,31,49,5,34,25,9,38,48,38,36,37,34,50,8,1,30}

    Returns: 562741504

  160. {27,7,20,6,13,24,10,18,30,28,13,20,10,1,1,20,26,32,31,31,4,7,6,39,13,23,16,15,37,38,33,18,22,15,33,4,44,40,29,16,26,17,37,49,12,11,16,12}

    Returns: 93711865

  161. {10,16,28,19,33,39,7,8,33,5,48,50,42,8,11,33,48,8,34,48,50,22}

    Returns: 904366324

  162. {41,28,10,18,1,35,13,45,38,29,40,2}

    Returns: 316371162

  163. {41,48,9,7,46,14,17,25,30,2,15,11,24,39,1,11,8,6,10,29,29,35,8,45,42,11,19,1,28,4,24,30,10,46,2,45,38,50,39,26,41}

    Returns: 43909898

  164. {34,37,27,32,45,16,19,47,41,47,25,3,40,6,23,26,30,15,20,10,38,2,7,10,16,49,2,48,36,27,35,32,18,24,6,30,10,11,29,21}

    Returns: 271121739

  165. {43,32,34,38,45,37,1,41,24,25,27,16,23,4,47,43,7,23,45,13,27,29,38,22,40}

    Returns: 645882733

  166. {21,36}

    Returns: 150390494

  167. {14,41,21,31,1,31,32,4,4,3,6,30,26,44,27,6,46,1,6,25,42,3,26,30,25,33,45,22,41,1,40,11,37,8,25,5,25,1,17,18,4,23,16,43,12,40,8}

    Returns: 739918998

  168. {30,2,19,2,1,18,30,8,45,9,35,15,46,31,36,21,13,29,44,27,25,38,24,5,8,13,2,22,28,1,27,4,40,41,40,22,19,35,13,14,13,1,44,6,23,31}

    Returns: 324508479

  169. {29,6,21,11,42,16,6,16,40,36,21,43,7,26,20,6}

    Returns: 320860739

  170. {42,10,49,47,10,40,17,30,21,35,30,16,19,15,3,49,46,7,15,35,18,36,19,1}

    Returns: 582406031

  171. {4,12,24,43,25,34,29,33,3,44,30,11,13,15,16,15,39,8,45,34,8,39,29,21,8,23,39,27,13,44,45,17,43,8,29,11,20,6}

    Returns: 945260178

  172. {13,32,25,47,10,15,41,17,25,9,20,17,9,26,27,43,38,46,27,30,39,16,7,25,44,49,12,39,21,28,34}

    Returns: 202471525

  173. {5,12,39,33,30,1,13,30,6,6,44,24,12,28,38,48,24,32,33,1,24,2,46,5,26,13,31,2,15,25,11,1,7,20,33,20}

    Returns: 251303483

  174. {47,14,38,33,12,20,22,42,11,15,10,26,35,44,39,50,34,33,2,38,28,37,17,9,47,36,26,49,34,26,38,18,35,35}

    Returns: 784334804

  175. {45,8,38,34,7,47,18,42,50,8,25,16,19,34}

    Returns: 793950011

  176. {11,46,33,29,25,8,4,30,25,48,42,27,40,14,49}

    Returns: 110192033

  177. {24,47,19,45}

    Returns: 745146991

  178. {23,37,23,1,1,16,1,17,21,30,15,11,22,35,14,11,21,31,1,10,32,1,21,29,6,22,22,30,20,28,35,2,11,37,42,24,1,35,34,9,1,23,26,35,5,37,27,36,28}

    Returns: 293019033

  179. {32,18,11,9,22,21,40,13,38,16,35,15,23,35,40,10,25,28,13,29,49}

    Returns: 251341320

  180. {25,14,13,20,24,1,26,26,20,33,43,32,12,20,9,14,49,33,44,25,44,27,48,34,41,18,4,1,47,15,12,40,12,27,25,47,33,18,24}

    Returns: 597273662

  181. {32,21,25,37,43,35,38,39,38,25,43,6,36,8,46,21,47,24,4,16,1,43,32,7,2,38,23,10,31,25,27,32,47,32}

    Returns: 498624653

  182. {30,35,11,8,31,33,21,29,2,20,13,7,8,33,14,42,5,34,1,39,25,49,1,10,23,20,41,23,9,31,39,32,5,46,21,28}

    Returns: 465755987

  183. {44,3,17,15,32,13,24,46,6}

    Returns: 981404340

  184. {13,15,25,28,17,49,26,8,46,14,16,22,10,26,41,49,35,24,36,34,32,37,42,31,34,9,24,21}

    Returns: 154083585

  185. {2,47,43,8,30,30,7,31,11,30,17,26,13,40,45,39,9,17,43,27,39,46,45,47,41,38,28,49,12,37,8,49,46}

    Returns: 111474050

  186. {50,48,12,44,3,49,34,45,12,29,38,23,37,7,23,44,14,49,24,21,26,31,30,35,31,3,47,35,45}

    Returns: 679657222

  187. {15,9,49,50,37,18,37,45,8,30,42,7,34,30,10,40,39,32,36,50,36,5,5,15,50,10,4,4}

    Returns: 722521119

  188. {22}

    Returns: 602640637

  189. {32,38,2,35,50,6,34,31,33,46,21,17,23,45,48,7,17,18,8,6,37,1,44,9,36,50,3,8,26,17,8,36,8,6,29,12,43,23,1,10,14,43}

    Returns: 569663321

  190. {12,18,5,15,6,12,50,1,19,40,45,29,14,14,33,41,29,26,45,30,19,18,36}

    Returns: 962591822

  191. {26,24,46,22,10,48,49}

    Returns: 491976355

  192. {20,48,1,41,32,15,23,46,44,4,7,6,3,6,47,40,9,26,10,25,48,44,28,6,39,3,4,4,31}

    Returns: 745539997

  193. {48,10,40,19,9,29,18,29,16,16,49,3,37,30,39,17,48,37}

    Returns: 438499612

  194. {34,4,10,34,16,2}

    Returns: 344608355

  195. {41,8,43,16,48,1,29,8,16,37,5,5,44,42,8,44,28,15,13,46,28}

    Returns: 202145946

  196. {37,47,38,18,5,6,8,27,34,38,14,9,30,14,16}

    Returns: 615177655

  197. {50,8,8,36,4,4,33,21,37}

    Returns: 248187445

  198. {38,46,6,21,23}

    Returns: 821358144

  199. {16,41,33,50,12,24,4,37,33,35,20,34,3,27,1,20,39,50,49,22,6,33,23,21,21,44,10,3,4,34,3,37,38,46,17,13,27,1}

    Returns: 809948774

  200. {39,30,11,49,22,18,27,30,25,43,33,4,30,29,21,9,6,33,34,43,40,49,32,44}

    Returns: 580110949

  201. {10,13,43,44,6,14,14,10,25,43,33,26,2,44,28,31,31,45,48,24,17,45,16,28,1}

    Returns: 988070081

  202. {23}

    Returns: 860734560

  203. {36,24,15,24,13,21,6,25,4,31,42,22,38,29}

    Returns: 40658443

  204. {34,35,13,41,46,41,17,47,39,41,46,16,33,37,32,38,28,12,42,15}

    Returns: 33006095

  205. {9,2,33,39,19,43,30,31,9,5,35}

    Returns: 173831460

  206. {15,27,1,27,27,18,37,42,50,31,38,5,9,2,50,32,46}

    Returns: 840515850

  207. {36,2,46,45,10}

    Returns: 101532183

  208. {30,31}

    Returns: 32680168

  209. {10,29,38,45,43,29,38,15,12,3,10,24,43,28,44,27,37,18,46,17,48,39}

    Returns: 364542596

  210. {48,25,30,49,36,8,5,2,24,12,30,30}

    Returns: 375799454

  211. {12,17,2,48,37,12,25,46,10,41,34,3,24,37,37,9,40,20,48,50,42,1,19,19,37,48,3,38,41,10,26}

    Returns: 744562556

  212. {42}

    Returns: 626855450

  213. {18,17,22,42,26,3,17,13,43,32,30,8,40,24,8,46,6,21,31}

    Returns: 236566588

  214. {2,15,19,48,4,45,32,4,44,25,30,32,26,43,35,7,43,37,28}

    Returns: 109626890

  215. {7,41,46,11,12,34,17,14,5,48,50,46,15,40,31,1,34,2,37,34,44,18,24,38,21,30,28,34,49,36,18,36,13,20,16}

    Returns: 152608507

  216. {13,13,14,41,4,29,9,31,3,21,47,34,25,28,38,9,7,5,39,36,41,42,34,47,27,18,31,30}

    Returns: 605161936

  217. {49,28,42,14,7,31,46,34,13,17,27,35,30,26,16,6,38,33,6,10,42,35,50,14,4,47,25,12,10,6,3,48,44,8,9,10,30,43,6,33,3,10}

    Returns: 250639800

  218. {47,44,9,36,6,3,24,2,17,35,4,41,11,10,12,37,16,32,12,10,20,17,29,28,16,45}

    Returns: 96714965

  219. {10, 10, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 23, 24, 25, 26, 26, 28, 28, 28, 50, 50, 49, 45, 5, 5, 5, 5, 5, 5, 5, 5 }

    Returns: 411445839

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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