Problem Statement

For a permutation $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$, define a length-$N$ integer sequence $f(P)$ as follows.

• Initialize an integer sequence $X$ with $X=(P_1,P_2,\dots,P_N)$. Repeat the following operation until $X$ is a strictly increasing sequence. (It can be shown that $X$ will be a strictly increasing sequence in a finite number of operations for any permutation $P$.) Let $C_x$ be the number of times an integer $x$ is moved to the end during this series of operations. Then, define $f(P)=(C_1,C_2,\dots,C_N)$.
• Let $k$ be the smallest index $i$ ($1 \leq i < N$) such that $X_i > X_{i+1}$. Move the $k$-th element of $X$ to the end. More precisely, replace $X$ with $(X_1,X_2,\dots,X_{k-1},X_{k+1},X_{k+2},\dots,X_N,X_{k})$.

Find the number, modulo a prime number $M$, of distinct sequences that can occur as $f(P)$.

Constraints

• $1 \leq N \leq 500$
• $10^8 \leq M \leq 10^9$
• $M$ is prime.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.