Parentheses and brackets P36384

Statement

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 $2 \le m \le 10^8$ .

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

Public test cases

Input

2 1 1000000
1 2 1000000
1 2 4
0 0 1000000
1 0 1000000
2 0 1000000
3 0 1000000
6 6 100000000
6 6 1000
50 50 100000000

Output

Information