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题库练习 PalindORme

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A14762 | $PalindORme$

时间限制1s

内存限制256MB

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题目描述

An integer array $a$ of length $n$ is said to be a PalindORme if ( $a_{1}$ $|$ $a_{2} $ $|$ $ \ldots $ $|$ $ a_{i}) = (a_{{n - i + 1}} $ $|$ $ \ldots $ $|$ $ a_{{n - 1}} $ $|$ $ a_{n}) $ for all $ 1 \leq i \leq n$ , where $|$ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR). An integer array $a$ of length $n$ is considered to be good if its elements can be rearranged to form a PalindORme. Formally, array $a$ is good if there exists a permutation $p_1, p_2, \ldots p_n$ (an array where each integer from $1$ to $n$ appears exactly once) for which $a_{p_1}, a_{p_2}, \ldots a_{p_n}$ is a PalindORme. Find the number of good arrays of length $n$ , consisting only of integers in the range $[0, 2^{k} - 1]$ , and print it modulo some prime $m$ . Two arrays $a_1, a_2, \ldots, a_n$ and $b_1, b_2, \ldots, b_n$ are considered to be different if there exists any $i$ $(1 \leq i \leq n)$ such that $a_i \ne b_i$ .

输入格式

The first and only line of the input contains three integers $n$ , $k$ and $m$ ( $1 \leq n,k \leq 80$ , $10^8 \lt m \lt 10^9$ ). It is guaranteed that $m$ is prime.

输出格式

Print a single integer — the number of good arrays modulo $m$ .

输入输出样例

输入 #1

1 1 998244353

输出 #1

输入 #2

3 2 999999733

输出 #2

输入 #3

7 3 796735397

输出 #3

输入 #4

2 46 606559127

输出 #4

C++ 编辑器

输入

输出