Description

Original Problem: HackerRank Equations

Find the number of positive integer solutions $(x, y)$ to the indeterminate equation:

Input Format

An integer $n$.

Output Format

An integer representing the number of valid pairs $(x, y)$. The answer should be modulo $10^9+7$.

Sample 1

There are three valid pairs $(x, y)$ that satisfy the equation: $(3,6),(4,4)$, and $(6,3)$.

2

3

Constraints and Hints

For $30\%$ of the data, $n\le 100$;
For all data, $1\le n\le 10^6$.