Nim
Two players play a game with a number of piles of stones, alternating turns. Each turn a player can choose to remove , , , or stones from a single pile; or alternatively they can choose to split a pile containing two or more stones into two non-empty piles. The winner is the player who removes the last stone.
A collection of piles is called a losing position if the player to move cannot force a win with optimal play. Define to be the number of distinct losing positions arising from piles of stones where each pile contains from to stones. Two positions are considered equivalent if they consist of the same pile sizes. That is, the order of the piles does not matter.
You are given and .
Find . Give your answer modulo .
取石子游戏
两位玩家正在玩一个游戏：游戏开始时有几堆石子，玩家轮流行动。每一回合，轮到行动的玩家可以从任一堆中移除、、或枚石子，或者将一堆至少两枚石子分成两个非空的堆。移除最后一枚石子的玩家获胜。
如果当前局面使得轮到行动的玩家在最优策略下仍无法获胜，则称之为必败态。定义为由堆、每堆包含至枚石子构成的不同必败态的数量。如果两个局面由相同大小的堆构成，则认为它们是相同的，换言之，计算必败态时不计堆的顺序。
已知，。
求，并对取余作为你的答案。
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