$k$-Nim 游戏的经典结论是，先手必败当且仅当把每堆石子的个数二进制拆分后，每一位上 $1$ 的个数都是 $k+1$ 的倍数。因此问题就变成了 $7^7$ 长度的 $7$ 进制不进位加法卷积快速幂。模 $998244353$ 存在 $7$ 阶单位根，故直接 $7$ 进制 FWT 即可，时间复杂度 $O(7^d\cdot (7\cdot d+\log K))$，其中 $d=7$。
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Discussion #190 for Problem #3088. Games
Type: Editorial
Status: Open
Posted by: jiangly
Posted at: 2025-12-13 00:01:08
Last updated: 2025-12-13 00:01:11
题解
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