Power Sum

Problem Description

You are given three numbers $n$, $m$, $p$. You need to compute $\sum\limits_{i=1}^{m} i^n \space \bmod \space p$.

Input Format

Three positive integers $n$, $m$, $p$. It is guaranteed that $p$ is prime and $p > n + 1$.

Output Format

One positive integer representing the result.

Sample Input

2 3 101

Sample Output

14

Hint

For $100\%$ of the data, $1\leq n\leq 2000$, $1\leq m, p \leq 10^9$.