Parentheses and brackets

Suppose that you have $x$ pairs of parentheses and $y$ pairs of brackets. In how many ways can you correctly put the parentheses and brackets?

For example, there are 15 ways with $x = 2$ and $y = 1$:

The number of combinations grows very fast with $x$ and $y$. Therefore, make the calculations modulo a given natural number $m$.

Input

Input consists of several cases. Every case has $x$, $y$ and $m$. Suppose $0 \le x \le 50$, $0 \le y \le 50$, and $2 \le m \le 10^8$.

Output

For every case, print the number of correct ways to place $x$ pairs of parentheses and $y$ pairs of brackets, modulo $m$.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T10:28:42.528Z

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