# 1735. Count Ways to Make Array With Product

<https://leetcode.com/problems/count-ways-to-make-array-with-product>

## Description

You are given a 2D integer array, `queries`. For each `queries[i]`, where `queries[i] = [ni, ki]`, find the number of different ways you can place positive integers into an array of size `ni` such that the product of the integers is `ki`. As the number of ways may be too large, the answer to the `ith` query is the number of ways **modulo** `109 + 7`.

Return *an integer array* `answer` *where* `answer.length == queries.length`*, and* `answer[i]` *is the answer to the* `ith` *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:**

* `1 <= queries.length <= 104`
* `1 <= ni, ki <= 104`

## ac

```java
```