Let $D(n)$ denote the number of divisors of n. $D(1) = 1, D(6) = 4$.

Let $F(N,K) = \displaystyle \sum_{i=1}^{N} D \left(i^K \right)$

You are given T tasks. Each task contains two integers, N and K. You have to output $F(N,K)$ modulo 10^9 + 7 for every task.

Input
First line contains a single integer T, the number of tasks.
Each of the next T lines contain two integers separated by a space, N, and K respectively.

Output
For each task, print $F(N,K)$ modulo 10^9 + 7 on a new line .

Constraints
$1 \leq T \leq 10^4$
$1 \le N,K \le 10^7$