Let $f(x,y)$ be the lowest common multiple of $x$ and $y$ and $g(x,y)$ be the greatest common divisor of $x$ and $y$. Determine $\sum _{x=1}^N\sum _{y=1}^{N}f(x,y)\times g(x,y{)}^2$ modulo a prime number, $K$.

Input Specification

The only line will contain two space-separated integers, $N$ $(1\le N\le {10}^{10})$ and $K$ $(2\le K\le 2\times {10}^9)$.

Output Specification

Output $\sum _{x=1}^N\sum _{y=1}^{N}f(x,y)\times g(x,y{)}^2$ modulo $K$.

Sample Input

10 131

Sample Output

64