You are given a $2$D integer array queries, where queries[i] = [n_i, k_i].

For each query, calculate the number of distinct arrays of positive integers of length $n_i$ such that the product of all elements equals $k_i$.

Return an integer array ans of the same length as queries, where ans[i] is the answer to the query queries[i] modulo $10^9 + 7$.

Constraints:

• $1 \leq$ queries.length $\leq 10^4$

• $1 \leq n_i, k_i \leq 10^4$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.