S-Nim 是 Arthur 和 Caroll 发明的一种类似 Nim 的游戏，玩家只能按预定义的集合 S 中的数移除珠子。如果在某次移动后，所有堆的珠子数量的异或和为 0，则该位置为输家位置。任务是确定给定的 S-Nim 位置是输家位置还是赢家位置。对于每个位置，如果至少有一种移动到输家位置，则该位置是赢家位置；否则，它是输家位置。
Problem Description
Arthur and his sister Caroll have been playing a game called Nim for some time now. Nim is played as follows:
The starting position has a number of heaps, all containing some, not necessarily equal, number of beads.
The players take turns chosing a heap and removing a positive number of beads from it.
The first player not able to make a move, loses.
Arthur and Caroll really enjoyed playing this simple game until they recently learned an easy way to always be able to find the best move:
Xor the number of beads in the heaps in the current position (i.e. if we have 2, 4 and 7 the xor-sum will be 1 as 2 xor 4 xor
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