Summing a Multiplicative Function

Define a multiplicative function \(f(x)\) such that for any prime \(p\) and positive integer \(k\), \[ f(p^k) = p^k (p^k - 1), \] and for \(n=1\) we define \(f(1)=1\) (by convention for multiplicative functions). For any positive integer \(n\), it holds that if \(n = \prod_{i=1}^r p_i^{k_i}\), then \[ f(n) = \prod_{i=1}^r \left(p_i^{k_i}(p_i^{k_i} - 1)\right). \] Your task is to compute

[ S(n) = \sum_{i=1}^{n} f(i)]

and output the answer modulo (10^9+7).

Note: You may assume that \(1 \le n \le 10^6\).

inputFormat

The input consists of a single integer \(n\) on one line.

outputFormat

Output a single integer, the value of \(S(n)\) modulo \(10^9+7\).

sample

1

1