**Time limit:**0.50 s**Memory limit:**512 MB

For example, if $n=9$, one possible structure is $[(2)(4)][(3)]$. In this case there are two chapters. The first chapter contains two sections with $2$ and $4$ pages, and the second chapter contains one section with $3$ pages.

Your task is to calculate the total number of possible structures for the book. Since the answer may be large, output it modulo $m$.

**Input**

The only input line contains two integers $n$ and $m$: the number of pages and the modulo.

**Output**

Print the total number of structures modulo $m$.

**Constraints**

- $1 \le n,m \le 10^9$

**Example**

Input:

`3 123`

Output:

`9`

Explanation: There are 9 possible structures: $[(3)]$, $[(1)(2)]$, $[(2)(1)]$, $[(1)(1)(1)]$, $[(1)][(2)]$, $[(2)][(1)]$, $[(1)][(1)(1)]$, $[(1)(1)][(1)]$ and $[(1)][(1)][(1)]$.