Statistics

Problem Statement for "FoxConnection2"

Problem Statement

There are N cities in Treeland. The cities are numbered 1 through N. The roads in Treeland have the topology of a tree. That is, there are exactly N-1 bidirectional roads in Treeland, each connecting a pair of cities, and it is possible to travel between any two cities along the roads.

You are given two int[]s A and B that describe the tree. Each of these int[]s has N-1 elements. For each valid i, there is a road that connects the cities A[i] and B[i].

Currently, k foxes live in a forest in Treeland. They would like to move into cities. Each fox must live in a different city. Therefore, they must select exactly k different cities where they will live. Additionally, they have an important constraint: The set of cities inhabited by the foxes must be connected. That is, for any two different cities i and j that both contain a fox, all the cities on the (only) path between i and j must also contain a fox.

Let X be the number of ways in which we can choose k cities in Treeland in such a way that the constraint is satisfied. Return the value (X modulo 1,000,000,007). Two selections are different if and only if there is a city selected in one of them but not in the other. (Note that we are only selecting a set of cities, we are not assigning individual foxes to the cities.)

Definition

Class:
FoxConnection2
Method:
ways
Parameters:
int[], int[], int
Returns:
int
Method signature:
int ways(int[] A, int[] B, int k)
(be sure your method is public)

Constraints

  • N will be between 2 and 50, inclusive.
  • A will contain exactly N-1 elements.
  • Each element of A will be between 1 and N, inclusive.
  • B will contain exactly N-1 elements.
  • Each element of B will be between 1 and N, inclusive.
  • The graph described by A and B will be a tree.
  • k will be between 1 and N, inclusive.

Examples

  1. {1,2,3}

    {2,3,4}

    2

    Returns: 3

    Treeland looks as follows: 1-2-3-4. There are 3 ways to put 2 foxes: {1,2}, {2,3} or {3,4}.

  2. {1,1,1,1}

    {2,3,4,5}

    3

    Returns: 6

    There are 6 ways: {1,2,3}, {1,2,4}, {1,2,5}, {1,3,4}, {1,3,5} and {1,4,5}.

  3. {1,2,3,4}

    {2,3,4,5}

    3

    Returns: 3

  4. {1,2,2,4,4}

    {2,3,4,5,6}

    3

    Returns: 6

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

    {2,3,4,5,6}

    5

    Returns: 4

  6. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40}

    20

    Returns: 923263934

  7. {2}

    {1}

    1

    Returns: 2

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

    {9,9,10,6,6,13,10,2,10,7,1,12,1,11,14}

    6

    Returns: 47

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

    {15,16,15,15,15,16,6,8,16,15,14,10,16,2,2}

    9

    Returns: 406

  10. {5,3,4,1,2}

    {6,6,3,6,4}

    4

    Returns: 4

  11. {21,22,16,37,33,25,20,14,38,36,34,43,8,26,29,15,10,27,18,28,47,35,1,9,45,7,4,3,42,32,41,17,31,5,48,49,12,30,23,39,11,40,19,50,6,2,24,46,44}

    {13,21,21,22,22,16,22,13,13,14,33,20,43,14,33,38,15,15,14,25,13,38,36,27,18,22,10,36,15,20,47,18,27,42,38,42,48,41,20,12,14,31,39,11,43,17,19,50,2}

    9

    Returns: 13705

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

    {3,3,11,7,7,3,21,8,20,18,3,5,19,10,14,2,3,7,21,12,19}

    14

    Returns: 1109

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

    {5,11,11,25,23,23,19,5,23,19,18,15,25,22,23,4,5,5,22,17,26,24,13,20,19}

    14

    Returns: 9556

  14. {3,24,13,1,4,16,6,14,18,17,23,2,12,8,9,7,5,22,21,20,11,19,10}

    {15,15,24,24,15,1,16,13,16,6,6,17,23,2,8,12,9,12,5,21,20,11,22}

    15

    Returns: 255

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

    {18,18,8,25,25,25,2,2,25,18,18,5,26,21,19,8,18,12,24,1,2,12,8,5,22,3}

    7

    Returns: 1068

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

    {18,11,21,18,18,16,21,7,15,11,2,18,17,5,22,5,11,24,21,19,18,9,25,25}

    11

    Returns: 3954

  17. {24,25,22,13,29,19,27,9,15,28,4,35,21,10,34,23,8,1,17,32,14,39,6,11,12,30,37,18,2,3,5,38,26,20,7,40,31,36,33}

    {16,24,16,16,16,16,22,19,22,24,19,4,16,35,10,9,16,15,9,22,29,16,22,25,27,15,15,27,13,10,37,17,23,39,17,18,17,19,14}

    36

    Returns: 7379

  18. {28,37,27,21,34,6,22,25,24,31,26,12,18,32,20,9,23,1,36,8,4,19,11,14,10,3,7,30,16,33,5,17,13,35,15,2}

    {29,28,37,37,37,28,34,34,22,21,21,24,29,18,22,26,34,34,6,6,31,22,26,24,24,23,19,1,3,9,30,8,16,24,26,23}

    30

    Returns: 97806

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

    {26,26,26,28,15,27,13,21,15,17,5,5,25,4,5,18,8,8,9,24,14,7,6,3,23,2,2}

    7

    Returns: 74

  20. {6,4,2,8,3,5,7}

    {1,1,4,2,8,8,3}

    6

    Returns: 5

  21. {4,3,5,2,6,7,9,1,8}

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

    5

    Returns: 6

  22. {41,32,10,35,18,14,20,12,25,44,48,40,26,23,42,28,17,37,22,16,19,39,8,30,31,11,34,43,45,1,46,5,13,3,15,9,29,50,47,38,21,6,24,4,49,36,27,33,7}

    {2,41,2,2,41,18,32,20,12,2,32,20,12,14,18,42,44,2,41,22,22,2,19,42,23,10,22,20,31,20,10,25,14,14,42,12,39,19,39,34,40,30,46,11,50,1,21,4,31}

    29

    Returns: 656399310

  23. {1}

    {2}

    1

    Returns: 2

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

    {10,25,10,28,2,7,25,16,25,7,10,14,9,27,22,9,3,25,14,2,16,20,1,8,4,26,3}

    18

    Returns: 17645

  25. {47,3,25,42,12,19,20,14,23,39,31,9,8,4,41,26,15,27,21,11,40,28,5,29,10,18,32,16,2,13,22,44,33,46,36,43,7,34,1,6,37,38,17,24,35,30}

    {45,47,47,47,3,3,45,20,25,20,25,23,25,14,20,41,41,9,31,39,4,8,8,14,23,21,9,12,9,3,10,42,2,27,3,32,41,27,26,31,18,31,39,5,28,1}

    10

    Returns: 22963

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

    {13,13,5,5,22,2,5,5,13,8,2,8,22,15,6,7,14,4,15,18,12,8,19}

    1

    Returns: 24

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

    {15,15,9,18,24,24,24,22,25,24,3,19,19,13,13,13,4,21,13,17,21,14,4,1}

    5

    Returns: 126

  28. {14,13,8,19,5,12,7,10,9,17,21,15,6,16,3,4,20,18,2,22,1}

    {11,14,14,13,8,5,12,7,10,9,17,17,15,15,6,16,3,4,20,18,22}

    2

    Returns: 21

  29. {23,22,5,27,15,28,2,25,10,11,7,18,21,14,26,29,8,32,16,9,20,17,31,1,4,12,3,6,24,30,13}

    {19,23,22,23,5,22,22,2,27,22,19,15,23,10,28,21,28,23,29,2,23,28,17,31,1,8,4,10,29,21,11}

    28

    Returns: 1899

  30. {4,3,5,2}

    {1,1,4,4}

    5

    Returns: 1

  31. {28,1,24,11,13,20,26,7,15,8,9,21,17,14,25,16,10,12,2,19,3,6,5,4,27,29,22,18}

    {23,28,28,1,24,23,11,1,7,7,15,15,9,24,9,25,15,13,14,2,8,7,14,15,12,2,4,4}

    14

    Returns: 22887

  32. {19,2,15,14,23,22,9,16,17,26,1,10,3,13,5,18,6,25,12,24,11,7,20,8,4}

    {21,19,2,19,19,21,2,15,22,23,22,15,9,9,16,22,3,2,23,2,14,18,22,9,26}

    20

    Returns: 7400

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

    {41,24,24,41,35,35,21,28,34,15,28,20,5,40,40,5,4,5,40,33,33,39,10,39,4,7,7,36,39,36,23,8,14,30,14,30,14,3,3,32,37,32}

    40

    Returns: 1219

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

    {8,8,31,8,8,21,16,34,25,4,42,35,25,33,13,16,21,16,19,31,35,21,19,24,41,15,41,10,23,3,7,19,17,18,13,38,24,29,15,5,2,29}

    12

    Returns: 82008

  35. {28,29,14,12,11,24,9,10,32,13,3,6,27,17,20,31,5,19,23,26,21,1,2,25,15,7,16,4,30,8,22}

    {18,28,28,18,18,18,11,24,10,24,28,29,11,18,12,11,29,3,32,5,10,32,17,32,5,23,19,6,2,23,4}

    1

    Returns: 32

  36. {22,31,14,29,28,9,5,23,6,27,36,34,7,18,20,11,19,25,10,2,15,32,26,16,4,8,3,17,1,24,35,21,12,13,33}

    {30,30,30,14,31,29,29,9,9,6,27,6,36,34,7,7,18,11,25,10,2,15,32,15,16,26,8,4,3,1,1,35,35,12,21}

    1

    Returns: 36

  37. {6,8,30,10,22,15,5,20,14,26,23,11,9,12,25,4,28,7,31,13,18,27,29,17,33,24,36,16,35,19,1,34,32,21,2}

    {3,3,6,3,10,3,3,22,10,8,15,5,8,14,11,25,4,5,12,25,26,28,12,25,28,31,7,24,17,13,27,16,36,17,19}

    26

    Returns: 74996

  38. {11,4,3,7,8,5,1,6,2,12,9}

    {10,11,11,3,3,7,8,5,1,6,2}

    1

    Returns: 12

  39. {2,1,5,4}

    {3,3,1,5}

    5

    Returns: 1

  40. {12,5,14,1,7,9,15,8,3,2,6,11,10,13}

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

    3

    Returns: 13

  41. {4,9,1,8,6,7,5,2}

    {3,4,3,1,9,1,6,5}

    8

    Returns: 3

  42. {10,24,27,38,21,5,28,35,3,17,49,31,15,11,7,33,22,48,23,29,9,46,39,47,32,36,2,20,42,43,4,34,16,25,45,1,6,18,41,12,44,37,26,8,14,13,19,40}

    {30,10,24,27,38,21,5,28,35,3,17,49,31,15,11,7,33,22,48,23,29,9,46,39,47,32,36,2,20,42,43,4,34,16,25,45,1,6,18,41,12,44,37,26,8,14,13,19}

    5

    Returns: 45

  43. {3,9,1,2,8,5,10,4,6,11}

    {7,7,7,1,7,9,2,5,9,8}

    4

    Returns: 20

  44. {16,3,8,26,11,25,20,28,10,23,17,29,7,1,24,14,18,5,9,15,22,27,12,13,4,6,19,2}

    {21,21,16,21,26,8,3,26,16,21,28,17,3,29,26,29,8,17,26,11,17,23,11,25,23,18,5,22}

    4

    Returns: 89

  45. {12,17,14,22,1,16,15,20,19,7,5,18,21,9,2,6,4,13,3,10,11}

    {8,8,17,17,8,17,16,12,16,22,22,1,19,7,18,21,9,6,9,18,6}

    20

    Returns: 46

  46. {22,1,16,21,14,27,5,3,2,37,12,35,29,10,38,23,13,18,9,6,4,34,36,31,11,8,28,19,20,33,26,24,15,30,32,17,25}

    {7,22,22,22,22,14,1,16,22,14,3,27,16,35,35,3,5,14,1,35,6,21,22,38,37,36,13,28,6,8,10,16,33,20,20,23,27}

    34

    Returns: 4086

  47. {7,12,14,4,9,3,6,13,11,1,10,8,5}

    {2,7,12,14,12,14,4,6,7,13,9,2,4}

    1

    Returns: 14

  48. {30,27,14,12,16,6,20,18,23,7,5,13,9,10,8,1,28,31,24,25,3,29,19,15,22,2,26,17,4,21}

    {11,11,11,30,12,14,6,27,20,18,23,5,20,9,9,8,1,10,10,10,24,25,29,25,3,15,15,26,26,15}

    16

    Returns: 12270

  49. {1,19,10,33,27,18,24,23,14,7,5,30,20,26,8,16,3,25,13,2,6,32,28,9,17,11,15,29,12,22,31,21}

    {4,4,1,19,1,19,33,24,23,14,23,7,5,30,26,26,8,16,25,16,2,13,32,2,6,17,9,15,15,11,29,29}

    21

    Returns: 4216

  50. {7,25,5,11,24,4,1,8,19,14,2,15,18,21,20,26,16,10,12,13,22,9,3,17,23}

    {6,6,7,25,11,6,25,25,6,19,5,14,8,1,19,8,26,20,15,15,21,13,9,20,22}

    4

    Returns: 58

  51. {6,5,1,2,8,4,7}

    {3,6,5,1,1,2,4}

    5

    Returns: 7

  52. {1,3,6,5,4}

    {2,2,1,6,1}

    5

    Returns: 3

  53. {21,17,14,39,4,33,7,45,13,32,41,3,28,6,12,47,46,11,42,44,43,38,24,29,2,10,8,34,27,23,30,18,25,15,36,31,20,19,37,35,26,16,1,9,40,5}

    {22,21,21,14,21,39,39,4,14,17,4,13,7,21,14,7,21,45,46,41,47,7,4,6,24,47,10,11,10,28,42,44,43,11,29,11,8,34,24,30,29,31,37,23,31,18}

    29

    Returns: 39336636

  54. {37,18,38,16,24,17,1,7,9,44,10,33,43,25,8,15,22,31,39,12,23,19,36,3,5,40,13,32,4,29,26,28,35,21,20,41,2,30,27,14,42,11,34}

    {6,37,18,38,18,16,37,17,37,1,44,24,38,16,1,9,7,10,44,7,7,39,16,7,24,1,3,33,12,7,17,1,29,44,22,7,35,8,15,23,10,7,35}

    41

    Returns: 1950

  55. {6,5,8,4,10,2,3,1,7}

    {9,9,5,9,6,9,5,4,8}

    1

    Returns: 10

  56. {20,2,12,6,9,1,4,8,21,10,3,11,29,23,26,17,30,28,5,32,31,14,25,16,15,18,33,7,24,27,19,13}

    {22,20,2,2,20,6,20,2,9,6,8,10,12,9,11,8,8,30,23,17,23,29,28,26,26,14,16,25,31,32,25,18}

    6

    Returns: 297

  57. {1,5,4,17,21,14,9,11,10,15,19,20,18,7,12,8,16,2,3,13}

    {6,1,5,4,5,4,5,21,21,10,14,15,15,10,7,19,8,8,16,3}

    15

    Returns: 491

  58. {2}

    {1}

    1

    Returns: 2

  59. {4,6,13,14,10,15,2,5,11,8,9,12,1,16,17,3}

    {7,4,6,6,13,10,6,13,7,2,11,14,12,4,1,13}

    12

    Returns: 175

  60. {3,4,1,2}

    {5,5,3,4}

    5

    Returns: 1

  61. {4,15,3,10,26,7,23,24,31,2,27,28,13,21,17,11,8,25,5,30,18,22,12,14,20,9,32,19,6,16,29,33}

    {1,4,15,4,3,4,7,15,1,3,23,7,31,2,13,26,21,10,4,15,25,4,13,12,1,30,3,10,7,14,16,21}

    4

    Returns: 119

  62. {1,5,3,4,2,8,7}

    {6,1,6,6,1,5,3}

    1

    Returns: 8

  63. {23,6,26,11,22,13,32,28,33,2,24,25,27,30,5,17,20,10,31,16,4,1,14,18,8,9,15,21,29,19,3,12}

    {7,7,7,26,26,22,6,32,22,28,13,2,2,27,24,30,27,30,30,17,10,4,10,16,14,1,8,14,9,29,29,21}

    6

    Returns: 161

  64. {26,12,33,15,8,28,44,4,23,40,19,2,42,34,6,31,39,1,11,7,29,47,46,3,5,25,22,45,35,36,48,21,32,13,16,37,38,27,10,41,14,18,20,30,9,24,17,43}

    {49,26,26,33,33,8,15,15,12,15,40,12,19,26,19,19,12,4,26,15,4,28,42,34,28,47,44,42,19,7,8,39,12,39,15,42,37,22,8,34,12,22,38,39,41,39,4,45}

    21

    Returns: 178542617

  65. {26,13,6,23,28,25,24,21,29,31,2,14,15,18,19,7,3,11,9,17,8,5,10,30,16,12,27,22,20,1}

    {4,26,13,26,4,6,25,25,6,26,6,24,29,2,13,21,24,26,2,21,26,9,13,2,13,30,26,7,12,2}

    21

    Returns: 346351

  66. {4,2,3}

    {1,1,2}

    2

    Returns: 3

  67. {1,4,5,3}

    {2,1,4,5}

    3

    Returns: 3

  68. {11,9,17,2,4,24,32,5,30,28,26,25,23,7,12,31,14,27,19,20,22,15,21,29,13,16,3,1,6,18,8}

    {10,10,11,10,11,10,2,17,5,24,9,9,2,30,32,28,4,23,12,17,10,9,24,17,17,20,22,19,16,22,22}

    2

    Returns: 31

  69. {4,17,8,40,34,10,15,1,3,21,16,11,35,38,14,25,31,22,37,19,36,6,43,28,26,18,39,20,12,32,9,44,30,29,24,27,42,5,2,33,7,13,41}

    {23,23,17,8,4,34,8,4,10,8,21,4,8,1,15,8,10,16,35,21,1,14,1,40,36,38,17,4,8,43,1,18,34,11,34,37,27,24,28,21,25,2,40}

    37

    Returns: 259800

  70. {28,13,15,24,25,16,20,9,5,8,11,1,6,3,12,4,18,29,2,30,10,27,22,7,32,23,21,14,31,26,19}

    {17,28,13,15,28,17,15,13,20,15,15,16,1,11,3,3,12,1,29,11,6,29,29,18,27,27,10,7,7,31,21}

    2

    Returns: 31

  71. {9,6,15,13,12,7,3,5,8,4,11,10,14,2,17,16,1}

    {18,9,6,9,15,15,6,7,9,6,4,4,11,14,3,11,8}

    10

    Returns: 612

  72. {2}

    {1}

    2

    Returns: 1

  73. {11,10,12,7,1,3,9,6,15,17,18,8,2,4,19,5,13,16}

    {14,11,14,10,14,12,1,3,7,1,11,18,12,12,3,9,11,13}

    16

    Returns: 118

  74. {6,1,3,2,7,5}

    {4,4,6,1,3,7}

    1

    Returns: 7

  75. {2,16,8,7,15,3,5,11,12,14,9,6,13,10,4,17}

    {1,2,2,8,7,15,7,15,3,12,5,14,14,13,13,10}

    9

    Returns: 68

  76. {2}

    {1}

    1

    Returns: 2

  77. {5,3,37,32,14,27,44,38,29,24,18,20,7,22,45,15,9,11,34,31,19,8,30,26,16,17,1,41,42,25,10,39,4,2,33,12,36,21,43,6,35,23,40,28}

    {13,13,13,5,5,37,3,32,32,29,37,32,18,27,38,18,45,20,15,15,22,11,34,9,31,31,16,31,8,1,1,10,1,42,42,33,25,39,12,36,36,43,36,36}

    22

    Returns: 604374

  78. {22,18,3,6,14,9,12,16,26,4,21,11,13,17,24,8,7,19,15,2,25,23,20,10,1}

    {5,5,5,18,18,22,9,9,16,14,4,21,26,13,11,14,16,22,3,16,8,17,11,4,7}

    20

    Returns: 1875

  79. {7,2,17,4,22,5,10,33,28,32,29,11,18,21,3,23,6,30,1,26,19,16,20,31,8,15,14,9,12,25,27,24}

    {13,13,7,17,17,2,13,5,7,17,22,33,17,4,2,29,32,23,5,17,21,5,16,30,26,19,22,8,20,9,26,8}

    1

    Returns: 33

  80. {4,12,18,1,15,20,10,2,8,11,3,7,5,17,6,19,21,22,16,9,14}

    {13,4,12,4,13,15,4,10,15,10,2,4,1,20,12,17,19,18,11,20,10}

    11

    Returns: 1667

  81. {10,20,13,28,3,26,19,1,12,6,5,9,24,23,17,22,27,7,14,21,11,8,4,15,16,2,18}

    {25,25,10,20,25,13,3,19,13,10,20,20,28,3,23,6,3,22,5,26,14,6,22,4,13,27,22}

    9

    Returns: 2095

  82. {13,17,9,16,5,6,28,27,20,21,4,31,34,14,22,12,24,10,25,23,19,8,3,29,18,11,2,33,7,30,32,26,1}

    {15,15,17,13,17,15,9,28,5,28,9,15,6,13,17,5,5,9,24,31,17,4,8,8,5,18,18,2,24,24,7,30,24}

    25

    Returns: 406579

  83. {35,6,1,22,32,33,38,16,23,5,36,12,9,25,29,17,26,4,11,18,34,2,8,14,3,15,21,20,31,13,10,30,37,19,7,27,28}

    {24,35,24,1,22,22,32,32,1,22,1,23,33,35,33,36,36,25,16,23,1,12,32,16,1,32,38,26,34,1,32,20,4,36,36,3,3}

    15

    Returns: 1840442

  84. {2,17,30,25,13,15,29,7,22,27,4,5,10,23,16,33,18,31,34,20,6,32,26,11,28,12,14,21,1,8,3,24,19}

    {9,9,2,9,30,2,25,15,7,7,15,9,13,17,13,4,16,27,13,22,15,25,18,2,34,15,11,5,30,26,31,6,3}

    24

    Returns: 134318

  85. {1,5,2,3}

    {4,4,1,2}

    2

    Returns: 4

  86. {23,29,28,7,43,21,44,26,25,17,41,34,14,39,18,42,36,27,6,45,5,31,10,35,11,9,38,24,3,2,37,12,30,22,32,13,4,20,16,19,8,1,15,33}

    {40,40,23,40,29,40,43,7,44,25,17,23,44,7,43,14,14,39,23,29,34,17,21,18,42,18,44,6,25,27,21,44,2,34,39,6,37,31,22,11,16,6,6,19}

    24

    Returns: 20383362

  87. {8,1,2,5,9,6,7,4}

    {3,3,8,2,1,5,9,9}

    5

    Returns: 6

  88. {13,10,11,5,24,6,30,20,3,16,4,2,14,22,7,26,1,19,18,15,29,12,9,25,21,8,28,27,23}

    {17,13,13,11,13,5,11,6,20,11,3,24,13,17,20,2,3,6,26,13,15,3,16,2,4,12,8,19,12}

    22

    Returns: 29338

  89. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40}

    18

    Returns: 21117453

  90. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2}

    {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}

    20

    Returns: 250632153

  91. {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}

    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,3,1}

    22

    Returns: 608335282

  92. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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 }

    20

    Returns: 923263934

  93. {1, 2, 3 }

    {2, 3, 4 }

    2

    Returns: 3

  94. {1, 1, 1, 2, 2, 2, 7, 8, 9, 9, 11, 4, 4 }

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

    5

    Returns: 33

  95. {1, 2, 2, 4, 4 }

    {2, 3, 4, 5, 6 }

    3

    Returns: 6

  96. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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 }

    47

    Returns: 18424

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

    2

    Returns: 39

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