Statistics

Problem Statement for "CycleColoring"

Problem Statement

This problem statement contains superscripts and/or subscripts. It may not display properly outside the applet.


Today, Bob is trying to count the colorings of a strange graph. It looks like a cycle of cycles.


The graph has two types of edges -- solid edges and dashed edges.


The edges between the vertices of the original cycles are all solid edges.
The edges that connect cycles together are all dashed edges.


More precisely, the graph consists of N cycles. The cycles are labelled, in order, as C0, C1, ..., CN-1. You are given a int[] vertexCount with N elements. Cycle Ci has vertexCount[i] vertices. The vertices of cycle Ci are labelled, in order, as vi, 0, vi, 1, ..., vi, vertexCount[i]-1. Note that the last vertex in this order is also connected to the first one. All of the edges that form these cycles are solid edges.


You are also given two int[]s fromVertex and toVertex, with N elements each. These int[]s describe the connection between cycle Ci and Ci+1 as follows: The vertex in cycle Ci with label vi, fromVertex[i] and the vertex in cycle Ci+1 with label vi+1, toVertex[i] will be connected with a dashed edge.


Bob has K distinct colors. He wants to know how many different ways there are to color the vertices of the graph under the following two rules:

  • Vertices connected with a solid edge must be colored using a different color.
  • Vertices connected with a dashed edge must be colored using the same color.

Two colorings are considered different if there is a vertex vi, j which has a different color in each coloring. Let C be the number of colorings that correspond to the given rules. As C can be extremely large, you should compute and return the value (C modulo 1,000,000,007).

Definition

Class:
CycleColoring
Method:
countColorings
Parameters:
int[], int[], int[], int
Returns:
int
Method signature:
int countColorings(int[] vertexCount, int[] fromVertex, int[] toVertex, int K)
(be sure your method is public)

Notes

  • i+1 is considered modulo N - hence, references to cycle CN are referring to cycle C0.

Constraints

  • vertexCount will contain between 1 and 50 elements, inclusive.
  • vertexCount, fromVertex, and toVertex will all contain the same number of elements.
  • Each element of vertexCount will be between 3 and 1,000,000, inclusive.
  • Element fromVertex[i] will be between 0 and vertexCount[i] - 1, inclusive.
  • Element toVertex[i] will be between 0 and vertexCount[i+1] - 1, inclusive.
  • K will be between 2 and 1,000,000,000, inclusive.

Examples

  1. {3, 3}

    {0, 0}

    {0, 0}

    3

    Returns: 12

    This graph consists of two cycles of length 3. There are two dashed edges, each connecting vertex 0 of one cycle to vertex 0 of the other cycle. These two vertices must share the same color. We have 3 possibilities for that color. Once we fix it, we have 2 possibilities how to color the rest of each cycle. Hence, the answer is 3*2*2 = 12.

  2. {6}

    {4}

    {1}

    3

    Returns: 12

    This graph only has one cycle. Note that for N=1 there is still one dashed edge and it connects two vertices on the same cycle. The 12 valid colorings of the resulting graph correspond to the 12 valid colorings of the graph from Example 0.

  3. {3, 3}

    {0, 1}

    {1, 2}

    3

    Returns: 0

    Vertices 0 and 2 on cycle 0 must both have the same color as vertex 1 on cycle 1. However, vertices 0 and 2 on cycle 0 are adjacent and therefore must have different colors. This is a contradiction. Therefore, there are no valid colorings of this graph.

  4. {9, 5}

    {8, 3}

    {0, 2}

    8

    Returns: 589124602

  5. {14, 15, 16, 17}

    {5, 10, 4, 6}

    {10, 3, 14, 10}

    614

    Returns: 818050159

  6. {3, 3, 3, 6, 3}

    {1, 2, 2, 4, 0}

    {0, 2, 2, 2, 0}

    5

    Returns: 16932240

  7. {3, 3, 3, 6, 3}

    {1, 2, 2, 4, 0}

    {0, 2, 2, 2, 0}

    2381828

    Returns: 715170955

  8. {6, 3, 6, 4, 4}

    {0, 0, 3, 3, 3}

    {2, 2, 1, 1, 2}

    5

    Returns: 824664753

  9. {6, 3, 6, 4, 4}

    {0, 0, 3, 3, 3}

    {2, 2, 1, 1, 2}

    2381828

    Returns: 22184471

  10. {4, 4, 4, 5, 5}

    {2, 0, 2, 4, 1}

    {0, 2, 1, 2, 0}

    5

    Returns: 816790685

  11. {4, 4, 4, 5, 5}

    {2, 0, 2, 4, 1}

    {0, 2, 1, 2, 0}

    2381828

    Returns: 803914433

  12. {6, 4, 6, 6, 5}

    {2, 3, 3, 0, 2}

    {2, 0, 5, 0, 2}

    5

    Returns: 944933078

  13. {6, 4, 6, 6, 5}

    {2, 3, 3, 0, 2}

    {2, 0, 5, 0, 2}

    2381828

    Returns: 412597157

  14. {4, 4, 5, 4, 3}

    {0, 0, 2, 2, 1}

    {0, 4, 3, 2, 2}

    5

    Returns: 344719440

  15. {4, 4, 5, 4, 3}

    {0, 0, 2, 2, 1}

    {0, 4, 3, 2, 2}

    2381828

    Returns: 875429929

  16. {46, 35, 45, 31, 60}

    {23, 16, 14, 16, 36}

    {11, 14, 26, 38, 37}

    2

    Returns: 0

  17. {46, 35, 45, 31, 60}

    {23, 16, 14, 16, 36}

    {11, 14, 26, 38, 37}

    3

    Returns: 407671109

  18. {46, 35, 45, 31, 60}

    {23, 16, 14, 16, 36}

    {11, 14, 26, 38, 37}

    17

    Returns: 804533889

  19. {46, 35, 45, 31, 60}

    {23, 16, 14, 16, 36}

    {11, 14, 26, 38, 37}

    999999999

    Returns: 993864615

  20. {30, 32, 58, 43, 41}

    {4, 15, 45, 36, 18}

    {22, 37, 10, 18, 5}

    2

    Returns: 0

  21. {30, 32, 58, 43, 41}

    {4, 15, 45, 36, 18}

    {22, 37, 10, 18, 5}

    3

    Returns: 293838890

  22. {30, 32, 58, 43, 41}

    {4, 15, 45, 36, 18}

    {22, 37, 10, 18, 5}

    17

    Returns: 759274862

  23. {30, 32, 58, 43, 41}

    {4, 15, 45, 36, 18}

    {22, 37, 10, 18, 5}

    999999999

    Returns: 970815448

  24. {40, 32, 38, 38, 48}

    {11, 29, 36, 34, 15}

    {21, 10, 2, 41, 7}

    2

    Returns: 2

  25. {40, 32, 38, 38, 48}

    {11, 29, 36, 34, 15}

    {21, 10, 2, 41, 7}

    3

    Returns: 139146514

  26. {40, 32, 38, 38, 48}

    {11, 29, 36, 34, 15}

    {21, 10, 2, 41, 7}

    17

    Returns: 738405059

  27. {40, 32, 38, 38, 48}

    {11, 29, 36, 34, 15}

    {21, 10, 2, 41, 7}

    999999999

    Returns: 684810955

  28. {4, 4, 4, 4, 4, 4, 4}

    {3, 0, 0, 3, 1, 2, 1}

    {1, 0, 3, 1, 3, 1, 0}

    2

    Returns: 0

  29. {4, 4, 4, 4, 4, 4, 4}

    {3, 0, 0, 3, 1, 2, 1}

    {1, 0, 3, 1, 3, 1, 0}

    3

    Returns: 209952

  30. {4, 4, 4, 4, 4, 4, 4}

    {1, 0, 2, 0, 3, 1, 1}

    {0, 0, 2, 3, 3, 0, 0}

    2

    Returns: 2

  31. {4, 4, 4, 4, 4, 4, 4}

    {1, 0, 2, 0, 3, 1, 1}

    {0, 0, 2, 3, 3, 0, 0}

    3

    Returns: 297432

  32. {4, 4, 4, 4, 4, 4, 4}

    {2, 1, 1, 3, 2, 2, 1}

    {1, 3, 3, 0, 0, 0, 2}

    2

    Returns: 0

  33. {4, 4, 4, 4, 4, 4, 4}

    {2, 1, 1, 3, 2, 2, 1}

    {1, 3, 3, 0, 0, 0, 2}

    3

    Returns: 244944

  34. {4, 4, 4, 4, 4, 4, 4}

    {3, 0, 3, 0, 2, 0, 3}

    {1, 0, 0, 0, 1, 3, 1}

    2

    Returns: 0

  35. {4, 4, 4, 4, 4, 4, 4}

    {3, 0, 3, 0, 2, 0, 3}

    {1, 0, 0, 0, 1, 3, 1}

    3

    Returns: 262440

  36. {4, 4, 4, 4, 4, 4, 4}

    {2, 1, 1, 3, 0, 3, 2}

    {0, 3, 0, 3, 0, 0, 2}

    2

    Returns: 2

  37. {4, 4, 4, 4, 4, 4, 4}

    {2, 1, 1, 3, 0, 3, 2}

    {0, 3, 0, 3, 0, 0, 2}

    3

    Returns: 288684

  38. {4, 4, 4, 4, 4, 4, 4}

    {3, 3, 0, 1, 0, 2, 1}

    {3, 2, 0, 0, 3, 1, 3}

    2

    Returns: 2

  39. {4, 4, 4, 4, 4, 4, 4}

    {3, 3, 0, 1, 0, 2, 1}

    {3, 2, 0, 0, 3, 1, 3}

    3

    Returns: 349920

  40. {4, 4, 4, 4, 4, 4, 4}

    {2, 2, 3, 1, 0, 2, 3}

    {2, 2, 3, 1, 0, 2, 2}

    2

    Returns: 0

  41. {4, 4, 4, 4, 4, 4, 4}

    {2, 2, 3, 1, 0, 2, 3}

    {2, 2, 3, 1, 0, 2, 2}

    3

    Returns: 262440

  42. {4, 4, 4, 4, 4, 4, 4}

    {2, 3, 0, 0, 2, 2, 1}

    {0, 2, 2, 3, 1, 1, 2}

    2

    Returns: 0

  43. {4, 4, 4, 4, 4, 4, 4}

    {2, 3, 0, 0, 2, 2, 1}

    {0, 2, 2, 3, 1, 1, 2}

    3

    Returns: 262440

  44. {4, 4, 4, 4, 4, 4, 4}

    {0, 3, 2, 1, 2, 2, 2}

    {2, 2, 2, 1, 3, 1, 3}

    2

    Returns: 2

  45. {4, 4, 4, 4, 4, 4, 4}

    {0, 3, 2, 1, 2, 2, 2}

    {2, 2, 2, 1, 3, 1, 3}

    3

    Returns: 288684

  46. {4, 4, 4, 4, 4, 4, 4}

    {2, 3, 3, 0, 3, 2, 2}

    {2, 3, 1, 2, 3, 0, 1}

    2

    Returns: 0

  47. {4, 4, 4, 4, 4, 4, 4}

    {2, 3, 3, 0, 3, 2, 2}

    {2, 3, 1, 2, 3, 0, 1}

    3

    Returns: 271188

  48. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2}

    {0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1, 1}

    2

    Returns: 0

  49. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2}

    {0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1, 1}

    3

    Returns: 536871936

  50. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2}

    {0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1, 1}

    4

    Returns: 12041987

  51. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2}

    {0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1, 1}

    100

    Returns: 89870415

  52. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2}

    {0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1, 1}

    1000000000

    Returns: 390121048

  53. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1}

    {0, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0}

    2

    Returns: 0

  54. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1}

    {0, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0}

    3

    Returns: 898994099

  55. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1}

    {0, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0}

    6

    Returns: 983223398

  56. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1}

    {0, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0}

    999

    Returns: 698029613

  57. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1}

    {0, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0}

    777777777

    Returns: 842177352

  58. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {2, 2, 1, 0, 2, 2, 2, 1, 1, 0, 2, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0}

    {1, 2, 1, 2, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 2, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0}

    7

    Returns: 77012778

  59. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {2, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 1, 0, 1, 1, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2}

    {0, 1, 2, 1, 0, 2, 2, 1, 1, 2, 2, 1, 0, 0, 2, 0, 2, 1, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1}

    7

    Returns: 712804721

  60. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 1, 2, 1, 0, 0, 1, 1, 2, 1, 1, 2, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 1, 0, 1, 1, 2, 0, 0, 2, 1, 2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2}

    {2, 1, 0, 0, 2, 0, 1, 1, 0, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0}

    7

    Returns: 712804721

  61. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 1, 1, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 1, 0, 2}

    {2, 2, 2, 1, 1, 2, 2, 0, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1}

    7

    Returns: 77012778

  62. {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}

    {0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1}

    {0, 2, 1, 1, 2, 0, 2, 2, 1, 0, 2, 1, 1, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 2, 0, 2, 2}

    7

    Returns: 703112740

  63. {976484, 854455, 965408, 964698, 800960, 924071, 905643, 860086, 784097, 756838, 889270, 765635, 765852, 897268, 800598, 757120, 931888, 788207, 802457, 903461, 834218, 967965, 842033, 956787, 765641, 964500, 990088, 896176, 782226, 957255, 767157, 952279, 901715, 795293, 761156, 855912, 969155, 884010, 815294, 840888, 888014, 994837, 908566, 853235, 904610, 972948, 967634, 822187, 932601, 948363}

    {255407, 222870, 819779, 319525, 278027, 347972, 180421, 523721, 145435, 532798, 605075, 254191, 157383, 462069, 36492, 680579, 467553, 536729, 33593, 480712, 284201, 84231, 596367, 71708, 528520, 854056, 36399, 435935, 647310, 794540, 474969, 121011, 719279, 169437, 579570, 820881, 227218, 869241, 53077, 620706, 283575, 934713, 170053, 267551, 337790, 524065, 449182, 94058, 921618, 411814}

    {49986, 956297, 425827, 573624, 813777, 764093, 131666, 277646, 460600, 8888, 704844, 196631, 173451, 45841, 621493, 769483, 612708, 597715, 756574, 464169, 792800, 666411, 911222, 550748, 948906, 507844, 725331, 101229, 597250, 550180, 306704, 398212, 112155, 459427, 604644, 357316, 220964, 597127, 333772, 776027, 967093, 826183, 105280, 236110, 746655, 812339, 494528, 664220, 383470, 78065}

    2

    Returns: 0

  64. {976484, 854455, 965408, 964698, 800960, 924071, 905643, 860086, 784097, 756838, 889270, 765635, 765852, 897268, 800598, 757120, 931888, 788207, 802457, 903461, 834218, 967965, 842033, 956787, 765641, 964500, 990088, 896176, 782226, 957255, 767157, 952279, 901715, 795293, 761156, 855912, 969155, 884010, 815294, 840888, 888014, 994837, 908566, 853235, 904610, 972948, 967634, 822187, 932601, 948363}

    {255407, 222870, 819779, 319525, 278027, 347972, 180421, 523721, 145435, 532798, 605075, 254191, 157383, 462069, 36492, 680579, 467553, 536729, 33593, 480712, 284201, 84231, 596367, 71708, 528520, 854056, 36399, 435935, 647310, 794540, 474969, 121011, 719279, 169437, 579570, 820881, 227218, 869241, 53077, 620706, 283575, 934713, 170053, 267551, 337790, 524065, 449182, 94058, 921618, 411814}

    {49986, 956297, 425827, 573624, 813777, 764093, 131666, 277646, 460600, 8888, 704844, 196631, 173451, 45841, 621493, 769483, 612708, 597715, 756574, 464169, 792800, 666411, 911222, 550748, 948906, 507844, 725331, 101229, 597250, 550180, 306704, 398212, 112155, 459427, 604644, 357316, 220964, 597127, 333772, 776027, 967093, 826183, 105280, 236110, 746655, 812339, 494528, 664220, 383470, 78065}

    15

    Returns: 39544823

  65. {976484, 854455, 965408, 964698, 800960, 924071, 905643, 860086, 784097, 756838, 889270, 765635, 765852, 897268, 800598, 757120, 931888, 788207, 802457, 903461, 834218, 967965, 842033, 956787, 765641, 964500, 990088, 896176, 782226, 957255, 767157, 952279, 901715, 795293, 761156, 855912, 969155, 884010, 815294, 840888, 888014, 994837, 908566, 853235, 904610, 972948, 967634, 822187, 932601, 948363}

    {255407, 222870, 819779, 319525, 278027, 347972, 180421, 523721, 145435, 532798, 605075, 254191, 157383, 462069, 36492, 680579, 467553, 536729, 33593, 480712, 284201, 84231, 596367, 71708, 528520, 854056, 36399, 435935, 647310, 794540, 474969, 121011, 719279, 169437, 579570, 820881, 227218, 869241, 53077, 620706, 283575, 934713, 170053, 267551, 337790, 524065, 449182, 94058, 921618, 411814}

    {49986, 956297, 425827, 573624, 813777, 764093, 131666, 277646, 460600, 8888, 704844, 196631, 173451, 45841, 621493, 769483, 612708, 597715, 756574, 464169, 792800, 666411, 911222, 550748, 948906, 507844, 725331, 101229, 597250, 550180, 306704, 398212, 112155, 459427, 604644, 357316, 220964, 597127, 333772, 776027, 967093, 826183, 105280, 236110, 746655, 812339, 494528, 664220, 383470, 78065}

    999999998

    Returns: 603362300

  66. {809047, 832465, 770961, 995308, 915602, 941685, 993186, 989356, 945009, 944937, 770659, 925465, 844362, 803633, 866134, 977708, 879276, 876150, 995072, 799233, 812423, 882079, 813654, 811137, 810715, 853716, 852774, 759409, 953782, 869619, 897169, 948566, 860301, 860354, 756649, 914255, 890457, 859596, 869471, 856707, 903283, 789428, 794067, 899064, 938159, 896696, 862550, 901529, 979626, 966105}

    {447116, 132726, 408397, 351036, 555901, 703424, 64669, 771014, 769210, 598206, 594950, 336003, 484337, 389645, 528572, 455279, 648934, 224257, 422256, 701196, 540131, 719210, 103072, 570080, 103010, 23084, 453224, 62822, 837918, 59271, 497957, 850248, 816218, 292414, 698093, 469086, 711216, 485869, 401117, 369850, 65117, 142197, 334011, 621198, 368431, 20271, 123185, 607918, 5787, 896858}

    {251627, 748003, 734971, 878162, 80586, 139706, 576647, 916473, 731779, 213283, 856692, 731103, 664798, 737711, 25278, 445542, 733902, 978293, 630840, 537621, 316433, 564984, 475948, 778221, 616857, 284762, 207603, 424708, 157221, 216146, 680165, 161154, 494603, 333007, 549028, 750137, 148068, 812663, 717530, 423423, 199771, 727021, 256312, 369357, 685598, 614012, 256515, 971658, 19590, 247607}

    2

    Returns: 0

  67. {809047, 832465, 770961, 995308, 915602, 941685, 993186, 989356, 945009, 944937, 770659, 925465, 844362, 803633, 866134, 977708, 879276, 876150, 995072, 799233, 812423, 882079, 813654, 811137, 810715, 853716, 852774, 759409, 953782, 869619, 897169, 948566, 860301, 860354, 756649, 914255, 890457, 859596, 869471, 856707, 903283, 789428, 794067, 899064, 938159, 896696, 862550, 901529, 979626, 966105}

    {447116, 132726, 408397, 351036, 555901, 703424, 64669, 771014, 769210, 598206, 594950, 336003, 484337, 389645, 528572, 455279, 648934, 224257, 422256, 701196, 540131, 719210, 103072, 570080, 103010, 23084, 453224, 62822, 837918, 59271, 497957, 850248, 816218, 292414, 698093, 469086, 711216, 485869, 401117, 369850, 65117, 142197, 334011, 621198, 368431, 20271, 123185, 607918, 5787, 896858}

    {251627, 748003, 734971, 878162, 80586, 139706, 576647, 916473, 731779, 213283, 856692, 731103, 664798, 737711, 25278, 445542, 733902, 978293, 630840, 537621, 316433, 564984, 475948, 778221, 616857, 284762, 207603, 424708, 157221, 216146, 680165, 161154, 494603, 333007, 549028, 750137, 148068, 812663, 717530, 423423, 199771, 727021, 256312, 369357, 685598, 614012, 256515, 971658, 19590, 247607}

    15

    Returns: 490996842

  68. {809047, 832465, 770961, 995308, 915602, 941685, 993186, 989356, 945009, 944937, 770659, 925465, 844362, 803633, 866134, 977708, 879276, 876150, 995072, 799233, 812423, 882079, 813654, 811137, 810715, 853716, 852774, 759409, 953782, 869619, 897169, 948566, 860301, 860354, 756649, 914255, 890457, 859596, 869471, 856707, 903283, 789428, 794067, 899064, 938159, 896696, 862550, 901529, 979626, 966105}

    {447116, 132726, 408397, 351036, 555901, 703424, 64669, 771014, 769210, 598206, 594950, 336003, 484337, 389645, 528572, 455279, 648934, 224257, 422256, 701196, 540131, 719210, 103072, 570080, 103010, 23084, 453224, 62822, 837918, 59271, 497957, 850248, 816218, 292414, 698093, 469086, 711216, 485869, 401117, 369850, 65117, 142197, 334011, 621198, 368431, 20271, 123185, 607918, 5787, 896858}

    {251627, 748003, 734971, 878162, 80586, 139706, 576647, 916473, 731779, 213283, 856692, 731103, 664798, 737711, 25278, 445542, 733902, 978293, 630840, 537621, 316433, 564984, 475948, 778221, 616857, 284762, 207603, 424708, 157221, 216146, 680165, 161154, 494603, 333007, 549028, 750137, 148068, 812663, 717530, 423423, 199771, 727021, 256312, 369357, 685598, 614012, 256515, 971658, 19590, 247607}

    999999998

    Returns: 500975551

  69. {770789, 985331, 941565, 810546, 977372, 952250, 877750, 925206, 778858, 984474, 916747, 789702, 873216, 940668, 971743, 998885, 763736, 937919, 752238, 784953, 756643, 827997, 851243, 858352, 931508, 751002, 907646, 798447, 819546, 946994, 864119, 947249, 995217, 937416, 766531, 825180, 859638, 908044, 920259, 833738, 883995, 794845, 983099, 805830, 826104, 990299, 832017, 828691, 978547, 957070}

    {592479, 280465, 477617, 336637, 903549, 686365, 270965, 725310, 215072, 840694, 816891, 238602, 634229, 68579, 771491, 87568, 376946, 253920, 618531, 365443, 656733, 644019, 167876, 764417, 6915, 240987, 557894, 315280, 219080, 566125, 700468, 217530, 93599, 388472, 254650, 109881, 809712, 640431, 68308, 601612, 803268, 332708, 694684, 176488, 756167, 492835, 643200, 127475, 458271, 901380}

    {769857, 707750, 399972, 827518, 436696, 428667, 426098, 78203, 171448, 152084, 719544, 156427, 844912, 591054, 665879, 218739, 86466, 388232, 12113, 5419, 141700, 354028, 292665, 690299, 151140, 170564, 376415, 114956, 618627, 271911, 132527, 521582, 151987, 232721, 364767, 359537, 544624, 670040, 796735, 199600, 708519, 236580, 567515, 102114, 457244, 666932, 332145, 655808, 683381, 750105}

    2

    Returns: 0

  70. {770789, 985331, 941565, 810546, 977372, 952250, 877750, 925206, 778858, 984474, 916747, 789702, 873216, 940668, 971743, 998885, 763736, 937919, 752238, 784953, 756643, 827997, 851243, 858352, 931508, 751002, 907646, 798447, 819546, 946994, 864119, 947249, 995217, 937416, 766531, 825180, 859638, 908044, 920259, 833738, 883995, 794845, 983099, 805830, 826104, 990299, 832017, 828691, 978547, 957070}

    {592479, 280465, 477617, 336637, 903549, 686365, 270965, 725310, 215072, 840694, 816891, 238602, 634229, 68579, 771491, 87568, 376946, 253920, 618531, 365443, 656733, 644019, 167876, 764417, 6915, 240987, 557894, 315280, 219080, 566125, 700468, 217530, 93599, 388472, 254650, 109881, 809712, 640431, 68308, 601612, 803268, 332708, 694684, 176488, 756167, 492835, 643200, 127475, 458271, 901380}

    {769857, 707750, 399972, 827518, 436696, 428667, 426098, 78203, 171448, 152084, 719544, 156427, 844912, 591054, 665879, 218739, 86466, 388232, 12113, 5419, 141700, 354028, 292665, 690299, 151140, 170564, 376415, 114956, 618627, 271911, 132527, 521582, 151987, 232721, 364767, 359537, 544624, 670040, 796735, 199600, 708519, 236580, 567515, 102114, 457244, 666932, 332145, 655808, 683381, 750105}

    15

    Returns: 41299226

  71. {770789, 985331, 941565, 810546, 977372, 952250, 877750, 925206, 778858, 984474, 916747, 789702, 873216, 940668, 971743, 998885, 763736, 937919, 752238, 784953, 756643, 827997, 851243, 858352, 931508, 751002, 907646, 798447, 819546, 946994, 864119, 947249, 995217, 937416, 766531, 825180, 859638, 908044, 920259, 833738, 883995, 794845, 983099, 805830, 826104, 990299, 832017, 828691, 978547, 957070}

    {592479, 280465, 477617, 336637, 903549, 686365, 270965, 725310, 215072, 840694, 816891, 238602, 634229, 68579, 771491, 87568, 376946, 253920, 618531, 365443, 656733, 644019, 167876, 764417, 6915, 240987, 557894, 315280, 219080, 566125, 700468, 217530, 93599, 388472, 254650, 109881, 809712, 640431, 68308, 601612, 803268, 332708, 694684, 176488, 756167, 492835, 643200, 127475, 458271, 901380}

    {769857, 707750, 399972, 827518, 436696, 428667, 426098, 78203, 171448, 152084, 719544, 156427, 844912, 591054, 665879, 218739, 86466, 388232, 12113, 5419, 141700, 354028, 292665, 690299, 151140, 170564, 376415, 114956, 618627, 271911, 132527, 521582, 151987, 232721, 364767, 359537, 544624, 670040, 796735, 199600, 708519, 236580, 567515, 102114, 457244, 666932, 332145, 655808, 683381, 750105}

    999999998

    Returns: 605351614

  72. {3}

    {0}

    {0}

    2

    Returns: 0

  73. {3}

    {0}

    {1}

    2

    Returns: 0

  74. {3}

    {0}

    {0}

    3

    Returns: 6

  75. {3}

    {0}

    {1}

    3

    Returns: 0

  76. {3}

    {0}

    {0}

    4

    Returns: 24

  77. {3}

    {0}

    {1}

    4

    Returns: 0

  78. {3}

    {0}

    {0}

    5

    Returns: 60

  79. {3}

    {0}

    {1}

    5

    Returns: 0

  80. {10}

    {0}

    {0}

    2

    Returns: 2

  81. {10}

    {0}

    {1}

    2

    Returns: 0

  82. {10}

    {0}

    {2}

    2

    Returns: 2

  83. {10}

    {0}

    {3}

    2

    Returns: 0

  84. {10}

    {0}

    {4}

    2

    Returns: 2

  85. {10}

    {0}

    {5}

    2

    Returns: 0

  86. {10}

    {0}

    {0}

    777

    Returns: 965860924

  87. {10}

    {0}

    {1}

    777

    Returns: 0

  88. {10}

    {0}

    {2}

    777

    Returns: 120403543

  89. {10}

    {0}

    {3}

    777

    Returns: 200641000

  90. {10}

    {0}

    {4}

    777

    Returns: 536228690

  91. {10}

    {0}

    {5}

    777

    Returns: 841059552

  92. {123182}

    {0}

    {0}

    2

    Returns: 2

  93. {123182}

    {0}

    {1}

    2

    Returns: 0

  94. {123182}

    {0}

    {123181}

    2

    Returns: 0

  95. {123182}

    {0}

    {2}

    2

    Returns: 2

  96. {123182}

    {0}

    {123180}

    2

    Returns: 2

  97. {123182}

    {0}

    {3}

    2

    Returns: 0

  98. {123182}

    {0}

    {4}

    2

    Returns: 2

  99. {123182}

    {0}

    {6664}

    2

    Returns: 2

  100. {123182}

    {0}

    {23817}

    2

    Returns: 0

  101. {123182}

    {0}

    {0}

    55

    Returns: 953759667

  102. {123182}

    {0}

    {1}

    77

    Returns: 0

  103. {123182}

    {0}

    {123181}

    77

    Returns: 0

  104. {123182}

    {0}

    {2}

    88

    Returns: 278511437

  105. {123182}

    {0}

    {123180}

    88

    Returns: 278511437

  106. {123182}

    {0}

    {3}

    99

    Returns: 564188445

  107. {123182}

    {0}

    {4}

    4837753

    Returns: 643832718

  108. {123182}

    {0}

    {6664}

    49938845

    Returns: 550114534

  109. {123182}

    {0}

    {23817}

    554534

    Returns: 115912927

  110. {1000000}

    {0}

    {0}

    1000000000

    Returns: 803957903

  111. {1000000}

    {999999}

    {0}

    55

    Returns: 0

  112. {3, 3}

    {0, 0}

    {0, 0}

    3

    Returns: 12

  113. {3, 3}

    {0, 0}

    {0, 1}

    3

    Returns: 0

  114. {3, 3}

    {0, 0}

    {0, 2}

    3

    Returns: 0

  115. {3, 3}

    {0, 0}

    {1, 0}

    3

    Returns: 0

  116. {3, 3}

    {0, 0}

    {1, 1}

    3

    Returns: 6

  117. {3, 3}

    {0, 0}

    {1, 2}

    3

    Returns: 6

  118. {3, 3}

    {0, 0}

    {2, 0}

    3

    Returns: 0

  119. {3, 3}

    {0, 0}

    {2, 1}

    3

    Returns: 6

  120. {3, 3}

    {0, 0}

    {2, 2}

    3

    Returns: 6

  121. {3, 3}

    {0, 1}

    {0, 0}

    3

    Returns: 0

  122. {3, 3}

    {0, 1}

    {0, 1}

    3

    Returns: 6

  123. {3, 3}

    {0, 1}

    {0, 2}

    3

    Returns: 6

  124. {3, 3}

    {0, 1}

    {1, 0}

    3

    Returns: 12

  125. {3, 3}

    {0, 1}

    {1, 1}

    3

    Returns: 0

  126. {3, 3}

    {0, 1}

    {1, 2}

    3

    Returns: 0

  127. {3, 3}

    {0, 1}

    {2, 0}

    3

    Returns: 0

  128. {3, 3}

    {0, 1}

    {2, 1}

    3

    Returns: 6

  129. {3, 3}

    {0, 1}

    {2, 2}

    3

    Returns: 6

  130. {466274, 44342}

    {0, 0}

    {0, 0}

    2

    Returns: 2

  131. {466274, 44342}

    {0, 0}

    {0, 1}

    2

    Returns: 0

  132. {466274, 44342}

    {0, 0}

    {0, 2}

    2

    Returns: 2

  133. {466274, 44342}

    {0, 0}

    {0, 3}

    2

    Returns: 0

  134. {466274, 44342}

    {0, 0}

    {0, 40}

    2

    Returns: 2

  135. {466274, 44342}

    {0, 0}

    {0, 92835}

    2

    Returns: 0

  136. {466274, 44342}

    {5, 0}

    {0, 0}

    2

    Returns: 0

  137. {466274, 44342}

    {6, 0}

    {0, 1}

    2

    Returns: 0

  138. {466274, 44342}

    {7, 0}

    {0, 2}

    2

    Returns: 0

  139. {466274, 44342}

    {8, 0}

    {0, 3}

    2

    Returns: 0

  140. {466274, 44342}

    {9, 0}

    {0, 40}

    2

    Returns: 0

  141. {466274, 44342}

    {466000, 0}

    {0, 92835}

    2

    Returns: 0

  142. {466274, 44342}

    {0, 0}

    {0, 0}

    7

    Returns: 502952257

  143. {466274, 44342}

    {0, 0}

    {0, 1}

    7

    Returns: 0

  144. {466274, 44342}

    {0, 0}

    {0, 2}

    7

    Returns: 436080902

  145. {466274, 44342}

    {0, 0}

    {0, 3}

    7

    Returns: 916534282

  146. {466274, 44342}

    {0, 0}

    {0, 40}

    7

    Returns: 536390421

  147. {466274, 44342}

    {0, 0}

    {0, 92835}

    992342

    Returns: 240292964

  148. {4, 4, 4}

    {0, 0, 0}

    {0, 0, 0}

    3

    Returns: 648

  149. {4, 4, 4}

    {0, 0, 0}

    {0, 0, 1}

    3

    Returns: 0

  150. {4, 4, 4}

    {0, 0, 0}

    {0, 0, 2}

    3

    Returns: 432

  151. {4, 4, 4}

    {0, 0, 0}

    {0, 0, 3}

    3

    Returns: 0

  152. {4, 4, 4}

    {0, 0, 0}

    {0, 1, 0}

    3

    Returns: 0

  153. {4, 4, 4}

    {0, 0, 0}

    {0, 1, 1}

    3

    Returns: 324

  154. {4, 4, 4}

    {0, 0, 0}

    {0, 1, 2}

    3

    Returns: 108

  155. {4, 4, 4}

    {0, 0, 0}

    {0, 1, 3}

    3

    Returns: 324

  156. {4, 4, 4}

    {0, 0, 0}

    {0, 2, 0}

    3

    Returns: 432

  157. {4, 4, 4}

    {0, 0, 0}

    {0, 2, 1}

    3

    Returns: 108

  158. {4, 4, 4}

    {0, 0, 0}

    {0, 2, 2}

    3

    Returns: 324

  159. {4, 4, 4}

    {0, 0, 0}

    {0, 2, 3}

    3

    Returns: 108

  160. {4, 4, 4}

    {0, 0, 0}

    {0, 3, 0}

    3

    Returns: 0

  161. {4, 4, 4}

    {0, 0, 0}

    {0, 3, 1}

    3

    Returns: 324

  162. {4, 4, 4}

    {0, 0, 0}

    {0, 3, 2}

    3

    Returns: 108

  163. {4, 4, 4}

    {0, 0, 0}

    {0, 3, 3}

    3

    Returns: 324

  164. {4, 4, 4}

    {0, 0, 0}

    {1, 0, 0}

    3

    Returns: 0

  165. {4, 4, 4}

    {0, 0, 0}

    {1, 0, 1}

    3

    Returns: 324

  166. {4, 4, 4}

    {0, 0, 0}

    {1, 0, 2}

    3

    Returns: 108

  167. {4, 4, 4}

    {0, 0, 0}

    {1, 0, 3}

    3

    Returns: 324

  168. {4, 4, 4}

    {0, 0, 0}

    {1, 1, 0}

    3

    Returns: 324

  169. {4, 4, 4}

    {0, 0, 0}

    {1, 1, 1}

    3

    Returns: 162

  170. {4, 4, 4}

    {0, 0, 0}

    {1, 1, 2}

    3

    Returns: 270

  171. {4, 4, 4}

    {0, 0, 0}

    {1, 1, 3}

    3

    Returns: 162

  172. {4, 4, 4}

    {0, 0, 0}

    {1, 2, 0}

    3

    Returns: 108

  173. {4, 4, 4}

    {0, 0, 0}

    {1, 2, 1}

    3

    Returns: 270

  174. {4, 4, 4}

    {0, 0, 0}

    {1, 2, 2}

    3

    Returns: 162

  175. {4, 4, 4}

    {0, 0, 0}

    {1, 2, 3}

    3

    Returns: 270

  176. {4, 4, 4}

    {0, 0, 0}

    {1, 3, 0}

    3

    Returns: 324

  177. {4, 4, 4}

    {0, 0, 0}

    {1, 3, 1}

    3

    Returns: 162

  178. {4, 4, 4}

    {0, 0, 0}

    {1, 3, 2}

    3

    Returns: 270

  179. {4, 4, 4}

    {0, 0, 0}

    {1, 3, 3}

    3

    Returns: 162

  180. {1000, 1000, 1000, 1000, 1000, 999}

    {15, 999, 400, 500, 333, 666}

    {999, 17, 500, 400, 666, 0}

    2

    Returns: 0

  181. {1000, 1000, 1000, 1000, 1000, 999}

    {15, 999, 400, 500, 333, 666}

    {999, 17, 500, 400, 666, 0}

    3

    Returns: 9093884

  182. {1000, 1000, 1000, 1000, 1000, 999}

    {15, 999, 400, 500, 333, 666}

    {999, 17, 500, 400, 666, 0}

    4

    Returns: 602873903

  183. {1000, 1000, 1000, 1000, 1000, 999}

    {15, 999, 400, 500, 333, 666}

    {999, 17, 500, 400, 666, 0}

    12371723

    Returns: 91401620

  184. {50, 50, 50, 50, 50, 50, 50, 50}

    {0, 17, 13, 5, 20, 29, 29, 10}

    {0, 13, 41, 10, 0, 29, 11, 5}

    2

    Returns: 2

  185. {50, 50, 50, 50, 50, 50, 50, 50}

    {0, 17, 13, 5, 20, 29, 29, 10}

    {0, 13, 41, 10, 0, 29, 11, 5}

    3

    Returns: 250051536

  186. {50, 50, 50, 50, 50, 50, 50, 50}

    {0, 17, 13, 5, 20, 29, 29, 10}

    {0, 13, 41, 10, 0, 29, 11, 5}

    7777

    Returns: 917523747

  187. {50, 50, 50, 50, 50, 50, 50, 50}

    {0, 17, 13, 5, 20, 29, 29, 10}

    {0, 13, 41, 10, 0, 29, 11, 0}

    2

    Returns: 0

  188. {50, 50, 50, 50, 50, 50, 50, 50}

    {0, 17, 13, 5, 20, 29, 29, 10}

    {0, 13, 41, 10, 0, 29, 11, 0}

    3

    Returns: 134034342

  189. {50, 50, 50, 50, 50, 50, 50, 50}

    {0, 17, 13, 5, 20, 29, 29, 10}

    {0, 13, 41, 10, 0, 29, 11, 0}

    7777

    Returns: 690969167

  190. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 2

  191. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    3

    Returns: 468478431

  192. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    1000000000

    Returns: 70176540

  193. {482373, 283712, 883, 12834, 5, 5, 482734, 99912, 35881, 277590}

    {59283, 49782, 0, 0, 3, 2, 84791, 40017, 2263, 461}

    {150173, 709, 11108, 0, 4, 7, 5902, 712, 190232, 390331}

    479360784

    Returns: 763634309

  194. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}

    2

    Returns: 2

  195. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}

    3

    Returns: 750285719

  196. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}

    1000000000

    Returns: 414567136

  197. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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

    Returns: 0

  198. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 77770, 0, 0, 0, 0, 0, 20, 40, 60, 80, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 70, 80, 90, 660, 0, 0, 0, 0, 0, 10, 30, 50, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 999999}

    2

    Returns: 2

  199. {1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000, 1000000}

    {0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 77770, 0, 0, 0, 0, 0, 20, 40, 60, 80, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 70, 80, 90, 660, 0, 0, 0, 0, 0, 10, 30, 50, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 999999}

    3

    Returns: 969527374

  200. {123, 999999, 959, 494, 192, 5491, 1249, 124912, 123, 528, 1258, 125, 125, 124, 123, 998, 99994, 91249, 214, 941, 124, 124, 214, 132, 123 }

    {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, 1, 2, 9, 2, 3, 1, 2, 9, 2, 3, 1, 2, 9, 2, 3, 1, 2, 9, 2, 3, 1, 2, 2 }

    987665123

    Returns: 280003972

  201. {482373, 283712, 883, 12834, 5, 5, 482734, 99912, 35881, 277590 }

    {59283, 49782, 0, 0, 3, 2, 84791, 40017, 2263, 461 }

    {150173, 709, 11108, 0, 4, 7, 5902, 712, 190232, 59283 }

    479360784

    Returns: 127312021

  202. {3 }

    {0 }

    {0 }

    3

    Returns: 6

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