Statistics

Problem Statement for "GogoXBallsAndBins"

Problem Statement

Like all other software engineers, Gogo likes to play with bins and balls. He has N bins, numbered 0 through N-1. Yesterday, Gogo distributed all his balls into the bins, placing S[0] balls into bin 0, S[1] balls into bin 1, and so on. No two bins contained the same number of balls. It is possible that one of the bins contained zero balls.


This morning, Gogo attended a lecture about sorting. After he got home, he decided to rearrange the balls in his bins into sorted order. More precisely, he wanted to reach a state with T[0] balls in bin 0, T[1] balls in bin 1, and so on, such that the following two conditions are met:

  • T is a permutation of S
  • T is sorted in ascending order

When rearranging the balls, Gogo always moves them one ball at a time. In other words, in each move Gogo takes a single ball from one bin and places it into another bin. Gogo is very smart, so he always uses the smallest possible number of moves.


For example, when rearranging S = {2, 5, 0} to T = {0, 2, 5}, Gogo will make exactly 5 moves. One way of changing S to T in 5 moves: first Gogo will move 3 balls from bin 1 to bin 2, and then he will move 2 balls from bin 0 to bin 2.


You are given the int[] T and an int moves. We are interested in all possible initial configurations S such that Gogo would produce the final configuration T, and in doing so he would move a ball exactly moves times. Let C be the number of such configurations S. Since C may be very big, your method must compute and return the value (C modulo 1,000,000,009).

Definition

Class:
GogoXBallsAndBins
Method:
solve
Parameters:
int[], int
Returns:
int
Method signature:
int solve(int[] T, int moves)
(be sure your method is public)

Constraints

  • T will contain between 2 and 50 elements, inclusive.
  • Each element of T will be between 0 and 50, inclusive.
  • T will be given in a strictly ascending order. Note that this implies that all the elements of T will be distinct.
  • moves will be between 0 and 650, inclusive

Examples

  1. {1, 2, 3}

    1

    Returns: 2

    There are six different configurations S that produce T = {1, 2, 3}. Out of these six, two have the property that Gogo will produce T by moving exactly one ball. These two configurations are S = {1, 3, 2} and S = {2, 1, 3}.

  2. {1, 2, 3}

    2

    Returns: 3

  3. {1, 2, 3}

    3

    Returns: 0

  4. {1, 2, 3}

    0

    Returns: 1

  5. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

    64

    Returns: 625702391

  6. {0, 1}

    650

    Returns: 0

  7. {1, 2, 4, 8, 16, 32}

    30

    Returns: 27

  8. {16,27}

    10

    Returns: 0

  9. {16,27}

    11

    Returns: 1

  10. {16,27}

    12

    Returns: 0

  11. {14,28,47}

    13

    Returns: 0

  12. {14,28,47}

    14

    Returns: 1

  13. {14,28,47}

    34

    Returns: 0

  14. {14,28,47}

    33

    Returns: 3

  15. {14,28,47}

    30

    Returns: 0

  16. {14,28,47}

    19

    Returns: 1

  17. {14,25,26,30,41,42,48}

    3

    Returns: 0

  18. {14,25,26,30,41,42,48}

    4

    Returns: 1

  19. {14,25,26,30,41,42,48}

    67

    Returns: 0

  20. {14,25,26,30,41,42,48}

    66

    Returns: 252

  21. {14,25,26,30,41,42,48}

    53

    Returns: 0

  22. {14,25,26,30,41,42,48}

    15

    Returns: 4

  23. {2,4,5,8,12,13,15,17,18,20,23,30,33,36,37,39,40}

    183

    Returns: 0

  24. {2,4,5,8,12,13,15,17,18,20,23,30,33,36,37,39,40}

    182

    Returns: 636940557

  25. {2,4,5,8,12,13,15,17,18,20,23,30,33,36,37,39,40}

    147

    Returns: 860846526

  26. {0,1,3,4,7,8,9,11,12,13,14,15,17,18,21,22,23,24,25,26,27,28,29,31,32,34,35,37,38,39,40,41,43,45,46,47,50}

    447

    Returns: 0

  27. {0,1,3,4,7,8,9,11,12,13,14,15,17,18,21,22,23,24,25,26,27,28,29,31,32,34,35,37,38,39,40,41,43,45,46,47,50}

    446

    Returns: 52931379

  28. {0,1,3,4,7,8,9,11,12,13,14,15,17,18,21,22,23,24,25,26,27,28,29,31,32,34,35,37,38,39,40,41,43,45,46,47,50}

    247

    Returns: 737079885

  29. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43,44,45,46,47,48,49,50}

    627

    Returns: 0

  30. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43,44,45,46,47,48,49,50}

    626

    Returns: 364133310

  31. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43,44,45,46,47,48,49,50}

    460

    Returns: 930558557

  32. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,48,49,50}

    629

    Returns: 0

  33. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,48,49,50}

    628

    Returns: 848639124

  34. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,48,49,50}

    141

    Returns: 520073870

  35. {3,38}

    35

    Returns: 1

  36. {0,3,9}

    6

    Returns: 1

  37. {4,25,47,48}

    44

    Returns: 9

  38. {0,14,26,27,43}

    28

    Returns: 1

  39. {12,19,20,31,37,38,45}

    11

    Returns: 1

  40. {3,16,18,22,26,29,34,43}

    57

    Returns: 1224

  41. {4,6,7,10,17,18,22,27,29,41,43,49,50}

    49

    Returns: 1558144

  42. {4,17,19,23,24,26,28,31,33,34,37,39,40,41,42,46,47,50}

    104

    Returns: 145225638

  43. {1,4,5,6,11,13,17,20,21,23,25,30,32,33,35,36,37,41,43,45,48}

    8

    Returns: 10579

  44. {0,2,4,5,10,12,14,16,20,21,22,27,28,29,30,32,33,34,35,36,38,41,43,44,49}

    179

    Returns: 204398385

  45. {0,1,2,7,8,9,10,11,12,13,16,18,19,20,21,22,23,27,29,33,34,35,36,37,39,40,41,42,45,46,47,48,49,50}

    289

    Returns: 484218893

  46. {0,1,2,3,4,6,7,8,9,10,12,14,16,17,18,19,20,22,24,25,26,27,28,29,30,31,32,33,34,36,37,39,40,41,43,44,45,46,48,49}

    162

    Returns: 120178274

  47. {0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,26,27,29,30,31,32,34,35,38,39,40,41,43,44,45,46,48,49,50}

    351

    Returns: 583888807

  48. {0,1,2,5,6,7,8,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,39,40,41,43,44,46,47,48,49,50}

    443

    Returns: 360310628

  49. {0,1,2,3,4,5,6,7,8,9,10,11,12,15,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,35,38,39,40,41,42,43,44,45,46,47,48,49,50}

    500

    Returns: 663984887

  50. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,30,31,32,33,34,35,36,38,39,40,41,42,43,45,46,47,48,49,50}

    504

    Returns: 922856254

  51. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50}

    518

    Returns: 645742651

  52. {0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    582

    Returns: 69098103

  53. {1,2,4,8,16,32}

    32

    Returns: 0

  54. {1,2,4,8,16,32}

    33

    Returns: 36

  55. {1,2,4,8,16,32}

    50

    Returns: 0

  56. {1,2,4,8,16,32}

    49

    Returns: 36

  57. {1,2,4,8,16,32}

    44

    Returns: 0

  58. {1,2,4,8,16,32}

    36

    Returns: 4

  59. {1,3,9,27}

    1

    Returns: 0

  60. {1,3,9,27}

    2

    Returns: 1

  61. {1,3,9,27}

    33

    Returns: 0

  62. {1,3,9,27}

    32

    Returns: 4

  63. {1,3,9,27}

    5

    Returns: 0

  64. {1,3,9,27}

    20

    Returns: 1

  65. {1,4,16}

    2

    Returns: 0

  66. {1,4,16}

    3

    Returns: 1

  67. {1,4,16}

    16

    Returns: 0

  68. {1,4,16}

    15

    Returns: 3

  69. {1,4,16}

    7

    Returns: 0

  70. {1,4,16}

    12

    Returns: 1

  71. {1,5,25}

    3

    Returns: 0

  72. {1,5,25}

    4

    Returns: 1

  73. {1,5,25}

    25

    Returns: 0

  74. {1,5,25}

    24

    Returns: 3

  75. {1,5,25}

    6

    Returns: 0

  76. {1,5,25}

    20

    Returns: 1

  77. {0,1,2,4,8,16,32}

    48

    Returns: 0

  78. {0,1,2,4,8,16,32}

    49

    Returns: 216

  79. {0,1,2,4,8,16,32}

    54

    Returns: 0

  80. {0,1,2,4,8,16,32}

    53

    Returns: 252

  81. {0,1,2,4,8,16,32}

    52

    Returns: 0

  82. {0,1,2,4,8,16,32}

    51

    Returns: 180

  83. {1,2,3,5,8,13,21,34}

    61

    Returns: 0

  84. {1,2,3,5,8,13,21,34}

    62

    Returns: 1764

  85. {1,2,3,5,8,13,21,34}

    66

    Returns: 0

  86. {1,2,3,5,8,13,21,34}

    65

    Returns: 576

  87. {1,2,3,5,8,13,21,34}

    64

    Returns: 0

  88. {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50}

    1

    Returns: 0

  89. {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50}

    2

    Returns: 25

  90. {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50}

    339

    Returns: 0

  91. {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50}

    338

    Returns: 650550754

  92. {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50}

    299

    Returns: 0

  93. {0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50}

    84

    Returns: 871152276

  94. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49}

    1

    Returns: 0

  95. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49}

    2

    Returns: 24

  96. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49}

    313

    Returns: 0

  97. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49}

    312

    Returns: 439430588

  98. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49}

    53

    Returns: 0

  99. {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49}

    266

    Returns: 130742502

  100. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    649

    Returns: 0

  101. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    650

    Returns: 848639124

  102. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    648

    Returns: 842532037

  103. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    0

    Returns: 1

  104. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    1

    Returns: 48

  105. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    649

    Returns: 0

  106. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    324

    Returns: 363246878

  107. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    2

    Returns: 1221

  108. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    10

    Returns: 567543548

  109. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    125

    Returns: 977735127

  110. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    600

    Returns: 817002488

  111. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    500

    Returns: 263616800

  112. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    400

    Returns: 816072913

  113. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    300

    Returns: 830193386

  114. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    200

    Returns: 537176421

  115. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    612

    Returns: 761570740

  116. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    166

    Returns: 612249467

  117. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    486

    Returns: 508204389

  118. {1, 2, 4, 8, 16, 32}

    5

    Returns: 1

  119. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50}

    650

    Returns: 848639124

  120. {0, 1}

    650

    Returns: 0

  121. {0, 50}

    50

    Returns: 1

  122. {0, 50}

    0

    Returns: 1

  123. {0, 50}

    100

    Returns: 0

  124. {0, 50}

    650

    Returns: 0

  125. {0, 50}

    1

    Returns: 0

  126. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    1

    Returns: 49

  127. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    650

    Returns: 0

  128. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    626

    Returns: 0

  129. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    625

    Returns: 848639124

  130. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    624

    Returns: 842532037

  131. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    620

    Returns: 151760682

  132. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    500

    Returns: 346658127

  133. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    600

    Returns: 638051583

  134. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    400

    Returns: 637276200

  135. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    300

    Returns: 855331364

  136. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    312

    Returns: 727847426

  137. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    313

    Returns: 472284951

  138. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    200

    Returns: 286592737

  139. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    100

    Returns: 406578775

  140. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 50}

    8

    Returns: 925733380

  141. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 50}

    650

    Returns: 0

  142. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 50}

    649

    Returns: 848639124

  143. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 50}

    640

    Returns: 230513787

  144. {48, 50}

    2

    Returns: 1

  145. {0, 4, 12, 28}

    17

    Returns: 0

  146. {1, 2, 3 }

    2

    Returns: 3

  147. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 }

    342

    Returns: 0

  148. {1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46 }

    300

    Returns: 772593524

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