Product of GCDs

You are given $N$ and $M$. Write a program that computes the product of $\gcd(i, j)$ over every $i$ from $1$ to $N$ and every $j$ from $1$ to $M$.

$\prod_{i=1}^{N}\prod_{j=1}^{M}\gcd(i, j)$

The first line contains $N$ and $M$, separated by a space. ($1 \le N, M \le 15{,}000{,}000$)

Print the product modulo $10^9 + 7$ on the first line.