Return of the Cliquers

An undirected graph on $n$ vertices whose vertices are labeled with the distinct numbers $1, 2, \ldots, n$ is called a symmetric labeled cliquer when it satisfies both of the following conditions:

• every connected component is a clique (a complete graph);
• all of its connected components contain the same number of vertices.

Maurycy has drawn every symmetric labeled cliquer that can be built on $n$ labeled vertices. He now wants to grade each drawing with one integer from the set $\{1, 2, \ldots, m\}$ (two different cliquers may receive the same grade). In how many different ways can he assign the grades? Because the answer can be very large, print it modulo $10^9 - 401$.

The picture below shows every symmetric labeled cliquer for $n = 4$.

A single line contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^9$, $1 \le m \le 2 \cdot 10^9$), separated by one space: the number of vertices of each symmetric labeled cliquer and the number of available grades.

Print, on a single line, the number of ways to assign the grades, taken modulo $10^9 - 401$.