Description

We call a permutation $p_1, p_2, \dots, p_n$ of $1 \sim n$ "Magic" if and only if

Count how many permutations of $1 \sim n$ are "Magic". The answer may be large; output the value modulo $m$.

Input Format

One line contains two integers $n, m$, as described above.

Output Format

Output a single integer: the number of "Magic" permutations of $1 \sim n$ modulo $m$.

20 23 

16

Hint

Constraints
For $100\%$ of the data, $1 \le n \le 10^6$, $1 \le m \le 10^9$, and $m$ is a prime.

Translated by ChatGPT 5