Statistics

Problem Statement for "WarAndPeas"

Problem Statement

The card game War is usually played with 52 cards. Alice and Bob enjoy the game so much that they have modified it to use N cards, and they have changed the rules significantly. The rules of their game are as follows:


The cards are numbered from 0 to N-1. At the beginning of the game, each of the N cards is assigned to either Alice or Bob with equal probability. The choices are made independently of each other and there is no guarantee that the players will receive the same number of cards.


The game consists of a series of steps. In each step, a pair of cards is selected uniformly at random from all possible pairs that consist of two distinct cards. The owner of the lower-numbered card becomes the owner of both cards in the pair. (If that player already owned both cards, nothing changes, but it still counts as a step.)


The game ends as soon as all cards are owned by the same player. Note that the game can end without any steps if all cards are initially assigned to the same player.


Carol watches Alice and Bob play the game. She likes peas, so she has invented the following rules for herself: Before the beginning of the game Carol chooses a specific state, i.e., a specific way cards are distributed between Alice and Bob. At the beginning of the game and also after each step, if the current state is Carol's chosen state, she eats a pea.


You are given Carol's chosen state as a String state. For each valid i, state[i] is either 'A' or 'B', indicating whether card i is owned by Alice or Bob.


We are interested in the expected number of peas Carol will eat during a game. This number can always be written as p / q, where p and q are positive coprime integers. Let X be an integer such that X * q is congruent to p, modulo 1,000,000,007. Return the value (X mod 1,000,000,007).

Definition

Class:
WarAndPeas
Method:
expectedPeas
Parameters:
String
Returns:
int
Method signature:
int expectedPeas(String state)
(be sure your method is public)

Notes

  • It can be proved that for the given constraints the return value always exists and it is unique.

Constraints

  • N will be between 2 and 1000, inclusive.
  • The length of state will be exactly N.
  • Each character of state will be 'A' or 'B'.

Examples

  1. "AB"

    Returns: 250000002

    The game will never be in Carol's chosen state after a step. Therefore, Carol will only eat a single pea if the initial state of the game is her chosen state. This happens with probability 1 / 4, hence the expected number of peas Carol will eat is also 1 / 4. The correct return value is 250,000,002 because (4 * 250,000,002) mod 1,000,000,007 = 1.

  2. "BAB"

    Returns: 375000003

    The expected number of peas eaten by Carol is 3 / 8. The correct return value is 375,000,003 because (375,000,003 * 8) mod 1,000,000,007 = 3.

  3. "AABBBBB"

    Returns: 973437507

    Here the expected number of peas eaten by Carol is 119 / 640.

  4. "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"

    Returns: 500000004

    In this test case the expected number of peas eaten by Carol is 1 / 2.

  5. "BABABBABAAABABBBBABABBABAABAAABAABAAAABBBBBBABBBBAB"

    Returns: 330545639

    For this state Carol is expected to eat 3095183339246779 / 13989277223419852125116563456 peas.

  6. "BB"

    Returns: 500000004

  7. "AAA"

    Returns: 500000004

  8. "BBBB"

    Returns: 500000004

  9. "BBBBB"

    Returns: 500000004

  10. "AABABB"

    Returns: 546875004

  11. "AAAAAAA"

    Returns: 500000004

  12. "AAABAABB"

    Returns: 606510421

  13. "BBBBBABAA"

    Returns: 113002233

  14. "AABBABBABB"

    Returns: 82240514

  15. "ABBBBABBAAB"

    Returns: 748558413

  16. "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"

    Returns: 84346116

  17. "BBBABBBABBBBBBBABBABBBBBABBBBBBBBBBBBABBBBBBBBABBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBABAABBBABBBBBBABBBBBABBBBBABABBBBBAABBBBAABBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAABBBBBBBBBABBBBBBABBBBAABBABBAABBBBBBBBBBABABBBBBBABBBBBBBBBBBBBBABABBBBBBBBBBBBAAABBBBAABBBBBBABBABBBBBABBBABBBBBBBBBBBBABBABBBBAABBBBABBBBBBABBBBBABBBBBBABBBBBBBABBABBABBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBABBBABBBBBBABBBBBABBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBABBABBBBBBBBBBBBBBBBBABABBBBBBBBBBBBABBBBBBBBBABBBBBBBBBBBBBBABBBABBABBBBABBBABBBBBBBBBABBABBBBBBBBBBBBBABBBBBBBABBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBBABBBABABBBBBBABBABBBBBBBBABBBABBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBABBBBBBABBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBABAABBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBABBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBABBBBBBBBBBBBBBBBABAABBBBAB"

    Returns: 908927496

  18. "BABAAAABABBBBBABAABAABBBBBBAABABABBBBAABAAABABBBBAAABABAABBAAABBBBBAAABBBBAABAAAAAAAAAABBABBABAAAAABBAABBAAABBABBBBABBAABABABAABABBBABBBBAAAAAABBBAABBBBBBABBAABBBAAABBABBBAAAAABBABAABBBBBABBBBBABABBABBBBABABBAABBBAABBBBAABBAAABABABBBBAAAABBBBBABBAAABAABABBABAAAABABAAABBBBBAAAABABBBABBBABAAABAAAABBBABABAAAAAAABBBAAAAABABBAAAABBBBABBABBBBAAAABBBBAAABBAABAAABBBBBBAAABBAAAAABAABBBAABBAAAABABAAAAAABABBBBABAAAABAABBABAABAABBABAABBBABBABBBBABAABBABABBABBABBAAABAABBABABABAAAABBBBBBABBABAAAABAABAABBBABBBABAABAABBABABBBBBAAABBBBBABBAABABABAAAAABBAAABABBABBBBABAAABAABBBBAABAABBAABBBABABBBBABAABAAABBBBBBABABBAABAABAAAAAABBBBAABBABBAAAABABABAABBABBBBBBAABAAABBBABBBABBABABABBBABABABAAABBBABBBBABBBBBABABABAAABBBAABABBBBAABBBABBBBABBABBBBBABBABBBAABBAAAAABBABBABAABBBAAAAAAABBBABABAABABBAAAABABBBBBBBAAAABAABBAAABBBABBBBABBBBBBABABBBBABAABBBAABBABABABBABAAABBAABBBBAAABABABAAAAAABBBAABABAABBAABABABBBBAAAAAABBBBAAAABAAABBABABABAABBBABBABABBABBABAABBABBBAAAAABBBABBABBBABABABBBBABBBAAABBABBAAABAAAAABBAABAAB"

    Returns: 787327381

  19. "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"

    Returns: 805280100

  20. "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"

    Returns: 248118077

  21. "AAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAABAAAAABAABAABAAAAAAABAAAABAAAAAAABBAAABBAAAAAAAAAAAAAAAAAABAABAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAABAAABAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABABAAAAABAAAAAABAAAABAAAAAAAAAAAAAAABAAAAAAABAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAABAABAAAABAAAABAAAAAAAAAAAAABAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAABAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAABAABAAAAAABAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAABBAAAAAAAAAAAAAAAAAAAAAAAAABAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBAAABAAAAAAAAAAAAAABBAAAAABAAAAABAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBAAAAAA"

    Returns: 382012576

  22. "ABAABABAAAAABBABAAAAABABAAAAABBABAAAAABAAAAABAAAAAAAAAAAAAAAAAAAAAAABAAAAAAABBBAAAAAABBAAAAABAAAAABBAAAAABABAAABAAAAAABBAAAAAAAAAAAAABAAABAAAAAAAAAAAAABAAABAAAAAABABABAABBAAAAAAAAAABABABBAAAAAAAAAAABAABAAAAAABAAABBAAAAAAABBBAAABAAAAAAABBAAABAAAAAAAAAAAABAAAAAABAAABAAABAAAAABAAAABAAAABAABAABAAAAAAAAAAAABABABAAAAAAAAAAAAAABABAAABAAABBAAABAABAAAAAAABBAAAAAAAAABAAAAAAAAAAAABAAAAAAABBAAABBAAABBAAAAABABAAAAABABABAAAAAAAAAAAABAAAABAAABAAAAAAABAAAAABAAABBAAAAAABAAAABAAAAAAAAAAAABAAAABBBBAAAAAABAABAAAAABBAABAAAAAAAAABABABAAAABAAAAABBABAAABBAAAAAAABBAAAAAAAABAAAABABAAAABABBBAAAAABABABAAAABABAAAAAAAAAAABAABABBAAAAAAAAAAABBAABABAAAAAAABAAAAABAAAAAAABABBAABAAAAAAAAABAAAAAABAAAAAAAAAAAAAABAABAAAAAABBBBABAAAAAAAAAAAAAABBBAABAAABAAAAAAAAAAAAAAAAAAAABAABAAABAAABBABAABAABBABBABAAAAAAAAAAAAABABAAAAABABABAAAAABBAAAAABAAAAAAAAAAAAAABAAAABAAAAABAABAAAAAAAABBAABAAABAAAABAAAAAAAAAAAAAABAAAAABBBAAAAAAAAAABAAABAAAABAAAAAAAAAAABBAAAAAAAAAAABAABBAAAAAAAAAAAAABAAAAABBAAAAAABABAAAAABAAAABAAAAABAAAABAAABAABBBABABAA"

    Returns: 501628998

  23. "AAAAAAAAAAAAAAAAAAAAAABAAAAAAAABBAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAABAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAABBAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAABAAAAAAAAAAAAAAAAAAAAAAABAAAABAAAAAABAAAAAAAAAAAAAABAAAABAAAAAAAABBAAAAAAAAAAAAAAAAAAABAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAABAAAAAAABAAAAAAAABAAAAABBAAAAABAAAAAAAAAAAAAABBBAAAAAAAAABAAABAAAAAAAABAAAABAAAAAAABAAAAAAAAAAABAABAAAAAAAAAAAABAAAABAAAAAAAAAAAAAAAAABAAAABABAAAAAAAAAAAAAAAAAAAABAAAAAAAAABAAAAAAAAAAAAAAAAABAABAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAABAAAAAAAAAABAAABAAAAAAAAAAAAAAAAABABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAABAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAABABAAAAAABAAAAAAAAAAAAAAAAAAAAAABAABAAAAAAAAAAAAAAAAAAAABBAAAAAAAAABA"

    Returns: 844556285

  24. "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"

    Returns: 176138067

  25. "AAAABBAAAAAAAAAAAABABAAAAAAAAABAABAAAABAAAAAABAABAAAAAAAAAAAABBABAAAAABAAAAABAABBAAAABAABAABABBAAAAAAAAABBAAAAAABBAAABABAAABABAABAAAABAAAAAAAAAAAAAABAAAAAAAAABAAAABAAAAAABAABAAAAABBAABAAAAAAAABBAAABBAAAABBAAAABBAABBBAAAAAABAAAABAAAAABAAAAAAABABAABAAABAABAABAAAABAAAAAAAABABABAAAAAAAABAAAABAAABAAABAAAAAABAAABAAAAAABAAAAABBAAAAAAAAABAAAABABABAAAABBAAAABABABABABAAABABBABAABAAAAAAABAAAABAAAAAAAAAAABBABBAAAABAABAAAAABBAAAAAAAAAAAABABBAAAAAABBAAABAABAAAAAAAAABAABABAAAAAAAABABAAAABBAAAAAABAAAAAABAAABAAAAAAAAAAAAABABABAAAAAAAAAAAABBAABAAAAABAABAABABAAAABAABAAAAAAABAABABBAABAABABAAAAABAABBAAABBAAAAAABAAAAAAAAAAAAABBAAAAABABABBAAABAAAABBAABAABAAAAAAAAAAAAAABBAABBBBABBBAAAABBABAAABAAAAABAABAAAABBBAABAAABBBAAABABAAAAABABAABAABAAAAAAABAAAAAAAABAAAAAAABAABBAAAAABAAABAAAAAAABBAABAAABAAAABBAAAAAABABAAAAAABAAAAABAAAAABAAABBBAAABBBBAAAAAAAAABBAAAAABAAAAAABAABABBBAAAAAAABABAAAAAABAAAAABAAAAAAAAAAABBBABAAAAAABBBABBABAAABAAAAAAAAAAABAABBBAABBAAAABAAAABAAABABAAAAAAAAAAAAAAAAAAAAAAAAAAAABBAAAABAABBAAAABAA"

    Returns: 287961222

  26. "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"

    Returns: 343313596

  27. "AAAAAAABAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAABAAAAAABAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAABAAAABAAAAAAABAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAABBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAABAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABABAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAABAAAAAAAAAABAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAABAAAAAAAAAABAAAAAAAAAAAAAAAAAAAABAAA"

    Returns: 710158882

  28. "AAABAABAAAAAAAAAAAAAAAAAABABAAAAABAABABAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAABAAAAAAAAAAABAABABABAAAAABAAAAAAAAAAAAAAAABAAAAAAABAABAABBAAAABAAAAAAAAAABBABAAAABAAAAAAAAAAAAAAAAAAABBAAAAAAAAAAABAAAABAAABAABAAAAAAABABAAAAAAAAAAAAAAAABAAAAAAAAAABAABAAABBAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABAABBAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAABBAAABABAABAAAAABAAAABAAAAAAAAAAAAAAAABAAAAAAABAAAAAAAAAAAABAAAABABABAAAABAAAAAABAAAABABAABAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAABBAAAAAAAAAAABAAAAAAAAAAAAAABBAAABAAAAAAAAAAAAAAAAABAAABAABAAABBAAAAAAAABAAAAAAAAABAAAAAAABAAAAAAAAAAABAAAAAAAAAAAAAAAABAAAABAAAAABAAAAAAAAAABAAAAAAAAAAAAAABAABAAAABAAABAAAAAABAAAABAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAABBAAAAAAABAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAABABAAABAAAAAAAAABAAAAAABAAAAAABAAAAAAAAAAABAAAAAAAABAAABAAAAABAAAAAAAAAAABAAAAAAAABBAAAAAAAAAAAAAAAAAAABBBABAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAABAAAAABAAAAABAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABBAAAAABAAABBABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAABAAAAAAAAAAABAAAABAAAA"

    Returns: 174475194

  29. "AAABAAAAABABAABBAABAAAAAAAAAAABABAAAABAAABBAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAABAAABAAAAAAAABAAAAABAAABAAAAAABAAABAAABABAAABABBABAAAAAAABAABAAAAAABAAAAABAAAAAAAAAABAAABABAAAABAAAABAAAAABABABAAAAAAABAABAAAAABAABAAABAAAAAAAABABAABAABBAAAAAAAAAAABAAABBAAAAAAAABAAAAAAAAAAAAAABBAAAAAAAAABAAAAAABABBABAAAAABAABAAAAAAAAAAABAAAAAAABBABAABBAAABAAAAABAABBBBBBAAAAAAAAAAAAAABAABBBAABAAAAABAABBAAAAAAABAABAAAAABAAAAAAAABBAAAAAABAABAABAABAAABAAABAAABAAAABAAAAAAABBAAAAAAAAABBBAAAAAAAAAAABABAAAAAAAAABAAAAAAAAAAABAABAABAABABBABAAAAAAAAAABBBBAAAAAABAAAABAAABAAAAAABAABAAAABBABAAAABBAAAAAABAAAABBABAAAAAABAAAABAAAAAAAAAAAAAAAAAAABAAAAAAAABAAAAAABABAAABAAAAABAAAAAAABAAAAAABABAAAAAAAABBAAABAAABBAAAAAAABAABAAAABABAAAABAAAAAAAAABAAAABAAAAABAABAAAAABAABAABAAAABABAAAAAAABAAABAAAAABABAAABAABAAAAABAAABAABBAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBABAAAAAAAAAAABABAAABABBBAAABAAABAAAAABBAAAABBBAAAAAAAAAABBAAAABABBAABAAAAAAABAABBAAABABAAAAABAAAABAAAAAAAAABBBAAAAAAABABBAAAAAAABAAAAAABABAAAAAABABABAAAABBAAAAAABBAAAABBAABA"

    Returns: 861413962

  30. "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"

    Returns: 115457099

  31. "AAAAAAAAAABBBAABAABBABAAAABAAAAAAAAAAABAAAABAAAAAABBAABABABAAABAAAAAABAAAABBABAAAAAAAAAAAABAAAAAAAABAAAABAAABAAAAAAAAAAAAAAAAAAAAAAABAAABAAAAAAAAAAAABABAAAAABAABAAAAAAAAAAAABBAAAAABAAAAAAAAABAABAAAAAAAAAAAAAAAAABAAAAAAAAAAAABABBAAAAAAAABBBAAAAAAAAAAAAABABAAAAAAAAAAABBAAAAABAAAAAAAABAAAAAAAAAAAAAAAABAABBBBBAAABAAAABBBAAAAAAAAAAAAAAAAAAABAABBAAAAAABBAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAABAAAAAAAAAAAAAABAABAAAAAAABBAABBAAAAAAABAAABBAABAABAAAAAAAAAAAAABAAAAABAAAAAABAAAAAAAAAAAAAAAAABAABAAAAAAABAAAABAAAAAABAABAAAAAABAABBAAABAAAABAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAA"

    Returns: 874559208

  32. "AAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAABAAAABAAAAAA"

    Returns: 200602390

  33. "BBBABBBABBBBBBBBBAABBBBBBBBBBABBBBBBBABBABABABBBABBBBAABBBBBABBBBBBBBBBABBBBAABBBBBBBBBBBBBBABBBABBBBBBBBABBBABBBBBBBABABBBBBBBBABBBBBBABABBBBBBBBBBBAAABBBBBBBBBABBBABBBABBBBBBBBBBBBBBBBAABBBBABBBBBBBBBABABBABABBBBBABBABBBABBBBBBBBBBBBBBABBBBBABBBBBBBBBBAABBBBABABBBBABABBBABBBBBBAABBBBBBBBBBBBBBABBABBBABABBBBBBBBBBBBBABBBABBBBBBBABABBABABBBBBABBBBABBBBBBBABBAABABBABBBBBBBBBBABBBBBBBBBBABBBBABBABBBBBBBBBBBABBBBBBABBBBBBBBBBABBBBBBBABAAABBBBBBBBBBAABABBABBBABBBBBBBABBBBBABBBBBBBBBBBABBBBBBBABBBBBBBBBBBBBABBBBABBABBBBABBBABBABBBBABABABBBBABBBABABBABBAABABAABBBBBBBBABBBBABBBBBBBBBABBBABABBBBBBBBBABABBABBBBABBABABABBBABAAABBBBBBBBBBABBBBBBBBBBAABBAAABBBBBBBBBBABBABBAABB"

    Returns: 267969369

  34. "AAABABBBBAABABABAAAABBBBABBBABBBAABBAAABABBBBABAABBAABAABBABABBAABBABBBBAAABBBAABBBBBBBAABBBBAAABBBBBABABABBBBBAABAABBAABAABBABBBABBBABAABBBAABBABAAABABABBBABBAAABAABBBAAAAAABBBBABBAABABBBAAABAB"

    Returns: 686246586

  35. "ABBABBBBBBBBBBBBBAABABABBBBBAABBBBBBBBBBABBBBBBBBBBBBBAABBBBBBBBBBBBBBABBBBBBBBABBBABBBBABBABABBBBBBBBABBABBBBBBBBBAABAABBBABABBAABBAABBAABAABBBBBBBBBBBABBBBBABBBBBABBBBBBABABBBBAABBBBBBBBBBBBBBBBBBBABAAABBBBBBBABBBABBBBBABBBBBBBABBABBABABBBBBABABBBABBBBBABBBBBABBBBBBBBABBBBBBBABBB"

    Returns: 162030979

  36. "ABBAAABABAABAABAAABAAAABBBBBAAABBABABBBAAAAAAAAABAAAAABAABBAABAAABAAABABBABABABAAAAABABBAAABAAAABAABAAABABBAAABAABAAAABBAAABBAAABABAABAABABABABAAABABAAAAABAAABAAABAAABAAABBBAABAABBABABAAAABABBBAABABABBABABAABBAABAABAAABABBABBAAAABAABAABBBBBBABBBAAAAAAABAAAABBAAABAAAAABABAABBBAAAAAAABABAAAAAABBAABBAAAAABAAAAAABABBBAABAAAAABABABAAABBBAA"

    Returns: 305353472

  37. "AABBABAABBABAAABBBAAABAAABAABBBABBBAABAABABAAABABAAAABABBABBABBBBABBAABBBBBBABABBBABBBBBABAABAABAAABABAAABABBBABBABBBBBBBBAABBBB"

    Returns: 866172181

  38. "BBBBABBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBABABBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBABBBBBBBBBBBBBBBB"

    Returns: 394501647

  39. "BBBBBBBBABBBBBBBBBBBBBBBBBBBBABBBBBABBBBBABBBBBBBABBBBBBABBBBBBBBBBBBBBBBBAABBBBABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBBABBABBBBBBBBBBBBABBABBBBBABBBABBBBBBBBBBBBBBB"

    Returns: 276096901

  40. "AAAAAAAAAAAAAAABBBAAAAAABAAAAABAAABAAAAABAAABAAAABAAAABAAAAAAAAAABAAAABAAAAAAAAAAAABBAAAAABABBAAAAAAAABBABBAAAAAABAAAAAAABBAAAAAABAABAAAAAAAABAAABAAABBAAABAAABBAABAAAABBAAAABABAAAAABAABBAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAABABAABAAAABAAABAAAABAAAABAABABAAABBAABBAABAAAAAAAAAAAAAAABAAAAAABABAAABAAAAAAAAAAAABAAABABABAAAAABABAABAAAAAAAAABAAAABABAABAAAABAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBAAAAAAAAABBAAAAAAAAAAAAAABBAAAAAAAABAABABAAABBBAAAAAAAAA"

    Returns: 934957557

  41. "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB"

    Returns: 136489804

  42. "BAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

    Returns: 136489804

  43. "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"

    Returns: 500000004

  44. "BBBBABABBABBBBBAABBABBBBBBBBBBBBBBBBBBABBABABBBABBBBABBABBBBBAABABABAAAAABBBBBABBBBBAABBABBBBBBBBBBBBBBBBBBABBABBAAABBBBBBBABABBBBBABABABBBBBABBABBBBABBBBBBBBBBBBBABBBBBBBBABBBABBBBBBAABBBBAAABBABBBBBAAABBABBBBAABABBBBBBBAABBBBBBABABBBBAABABBBBBBAABBBBBBAABBABBBBBBBBBBBBBBBAAABBBBBBBBBBBABBAAABBBBAAAABBBABBBBBA"

    Returns: 21844

  45. "AAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

    Returns: 999972287

  46. "ABBBAAABBAAABBBB"

    Returns: 557412872

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.
This problem was used for: