Define function $f(n)$ as the sum of all factors of $n$, for example $f(1) = 1,f(5) = 1 + 5 = 6,f(6) = 1 + 2 + 3 + 6 = 12$.

Given $n$ and $k$, you need to calculate

$\sum_{i=1}^n f(i^k)$

Since the answer is too large, you need to output the remainder of the answer divided by $10^9+ 7$.

One line, two numbers $n$ and $k$, $(1≤n, k≤10^7)$

One line indicates the answer.

$f(1^2) +f(2^2) = (1) + (1 + 2 + 4) = 8$