证不出结论破防了，结果题解里怎么全是暴力猜结论，，这一题证明周期才是关键吧。

https://www.luogu.com.cn/article/lybarot5 by nyLittleT

https://www.luogu.com.cn/article/528x7oks by RP_INT_MAX

https://www.luogu.com.cn/article/yaef7y3c by No21

https://www.luogu.com.cn/article/8n15cahi by BugGod

https://www.luogu.com.cn/article/vh4ymgzl by Addicted_Game

以上题解都是暴力然后猜结论。

https://www.luogu.com.cn/article/jvvj1br5 by ny_Dacong

这一篇题解到最后还是用了周期，而且只说了一句 我们发现，周期是 2 的次方。

https://www.luogu.com.cn/article/skfjeolu by jifbt

没有证明。

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另外，本题结论有没有大佬能详细推一推，蒟蒻推不出来（）