Book writing |
| Time limit: | 0.50 s |
| Memory limit: | 512 MB |
|
Kaaleppi will write a book of $n$ pages. There will be some chapters and sections, so that each chapter contains one or more sections, and each section consists of one or more pages.
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
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 $[(1)][(1)][(1)]$.
