<p>You are given a 2D integer array, <code>queries</code>. For each <code>queries[i]</code>, where <code>queries[i] = [n<sub>i</sub>, k<sub>i</sub>]</code>, find the number of different ways you can place positive integers into an array of size <code>n<sub>i</sub></code> such that the product of the integers is <code>k<sub>i</sub></code>. As the number of ways may be too large, the answer to the <code>i<sup>th</sup></code> query is the number of ways <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> queries = [[2,6],[5,1],[73,660]]
<strong>Output:</strong> [4,1,50734910]
<strong>Explanation:</strong>&nbsp;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 10<sup>9</sup> + 7 = 50734910.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> queries = [[1,1],[2,2],[3,3],[4,4],[5,5]]
<strong>Output:</strong> [1,2,3,10,5]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= queries.length &lt;= 10<sup>4</sup> </code></li>
	<li><code>1 &lt;= n<sub>i</sub>, k<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
</ul>


class Solution {
public:
vector<int> waysToFillArray(vector<vector<int>>& queries) {
    vector<vector<int>> comb(10013, vector<int>(14, 0));
    const int mod = 1000000007;
    for (int n = 0; n < 10013; ++n) {
        comb[n][0] = 1;
    }
    for (int n = 1; n < 10013; ++n) {
        for (int r = 1; r < 14; ++r) {
            comb[n][r] = (comb[n - 1][r - 1] + comb[n - 1][r]) % mod;
        }
    }
    vector<int> primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97};
    vector<int> res(queries.size(), 1);
    for (auto i = 0; i < queries.size(); ++i) {
        int n = queries[i][0], k = queries[i][1];
        for (auto p : primes) {
            int r = 0;
            while (k % p == 0) {
                ++r;
                k /= p;
            }
            res[i] = (long)res[i] * comb[n - 1 + r][r] % mod;
        }
        if (k != 1)
            res[i] = (long)res[i] * n % mod;
    }
    return res;
}
};
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