Background

Problem Description

Given $n, m$, find

Input Format

Two integers $n, m$.

Output Format

Output one integer, representing the answer. The answer should be taken modulo $10^9+7$.

5 5

453

20 20

173825

Hint

$\sigma_0, \varphi$ are the divisor-counting function and Euler's totient function, respectively.

This problem may be slightly tight on constant factors.

Constraints

This problem uses bundled subtasks.

For all testdata, $1 \le n, m \le 3\times 10^6$.

For some reason, you only need to get $\ge 100$ points to pass this problem.

Translated by ChatGPT 5