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 $$D(1^2)+D(2^2)+D(3^2)+D(4^2)+D(5^2) = 1 + 3 + 3 + 5 + 3 = 15$$