SOLVE
LATER
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
\(1 \leq T \leq 10^4\)
\( 1 \le N,K \le 10^7 \)
In the first case, answer is \(D(1) +D(2)+D(3) = 1 + 2 + 2 = 5\).
In second case, answer is \(D(1^2)+D(2^2)+D(3^2)+D(4^2)+D(5^2) = 1 + 3 + 3 + 5 + 3 = 15\)