Problem Description

This is a simple and easy number theory problem.

$\text{lcm}(1,2,3,\cdots,n)$ denotes the least common multiple of all numbers from $1$ to $n$. Calculate the remainder of $\text{lcm}(1,2,3,\cdots,n)$ when divided by the prime number $p$.

Input

A single line containing two space-separated integers $n, p$ satisfying $1\leqslant n < p \leqslant 1\times 10^4$.

Output

Output a number representing $\text{lcm}(1,2,3,\cdots,n)~\%~p$.

Samples

5 7

4

1919 9973

2007