You are given \(n\) and \(x \Delta y = \frac{x \times y}{\gcd(x, y) ^ 2}\).
Print the value of \(\sum_{i = 1}^{n} \sum_{j = 1}^n i \Delta j \mod (10^9 + 7)\).
Input format
Output format
Print the value of \(\sum_{i = 1}^n \sum_{j = 1}^n i \Delta j \mod (10^9 + 7)\).
Constraints
\(1\le n\le10^{6}\)
1 * 1 / 1 + 1 * 2 / 1 + 2 * 1 / 1 + 2 * 2 / 4 = 6.