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
\(1 \leq T \leq 10^4\)
\( 1 \le N,K \le 10^7 \)