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Description

设$f(x,k) = x^k * \sigma(x^k)$,$\sigma(x)$是约数个数函数。

现在请你计算$\sum_{x=1}^{n}{f(x,k)}$在模$1e9+7$意义下的答案。

Input

一个$n$和一个$k$。

Output

输出一行代表最后的答案。

Samples

10 2

2419

Constraints

$1 \leq n \leq 1e10$

$0 \leq k \leq 100$

Resources

By Forsaken