Problem Statement

You are given an integer $N$ and a prime $P$.

Count the number, modulo $P$, of undirected connected graphs $G$ of $N$ vertices numbered $1$ to $N$ that satisfy the following condition:

• There are no self-loops in $G$. Note that multiple edges are allowed.
• For all edges $(u,v)$ in $G$, if we delete $(u,v)$ from $G$, $G$ remains connected. In other words, $G$ is edge-biconnected.
• For all edges $(u,v)$ in $G$, if we delete $(u,v)$ from $G$, $G$ is no longer edge-biconnected.

Two graphs are considered different if and only if there exists a pair of distinct vertices $(u,v)$ such that the numbers of edges connecting $u$ and $v$ in the two graphs are different.

Constraints

• $2 \le N \le 50$
• $10^9<P<1.01\times 10^9$
• $P$ is prime.
• All input values are integers.

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.