1735 - Count Ways to Make Array With Product.

Hard

You are given a 2D integer array, queries. For each queries[i], where <code>queriesi = n_i, k_i</code>, find the number of different ways you can place positive integers into an array of size <code>n_i</code> such that the product of the integers is <code>k_i</code>. As the number of ways may be too large, the answer to the <code>i^th</code> query is the number of ways modulo <code>10⁹ + 7</code>.

Return an integer array answer where answer.length == queries.length, and answer[i] is the answer to the <code>i^th</code> query.

Example 1:

Input: queries = \[\[2,6],5,1,73,660]

Output: 4,1,50734910

Explanation: Each query is independent.

2,6: There are 4 ways to fill an array of size 2 that multiply to 6: 1,6, 2,3, 3,2, 6,1.

5,1: There is 1 way to fill an array of size 5 that multiply to 1: 1,1,1,1,1.

73,660: There are 1050734917 ways to fill an array of size 73 that multiply to 660. 1050734917 modulo 10⁹ + 7 = 50734910.

Example 2:

Input: queries = \[\[1,1],2,2,3,3,4,4,5,5]

Output: 1,2,3,10,5

Constraints:

• <code>1 <= queries.length <= 10⁴</code>

• <code>1 <= n_i, k_i<= 10⁴</code>