<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) {
        long long choose[10050][33] = {0};           
        int mod = 1e9+7;            
        for (int j = 0; j != 10050; ++j) choose[j][0] = 1;  
        for (int n = 1; n != 10050; ++n) {
            for (int r = 1; r != 33; ++r) {
                choose[n][r] = (choose[n - 1][r - 1] + choose[n - 1][r]) % mod;
            }
        }
        vector<int>primes;
        vector<bool>sieve(10001,true);
        sieve[1]=false;
        for(int i=2;i<10001;i++){
            if(sieve[i]==false) continue;
            for(int j=i*2;j<10001;j+=i){
                sieve[j]=false;
            }
        }
        for(int i=2;i<10001;i++) if(sieve[i]==true) primes.push_back(i);
        vector<int>final;
        vector<long long>fact(15);
        fact[0]=1;
        for(int i=1;i<15;i++) fact[i]=fact[i-1]*i;
        for(auto it : queries){
            int num=it[1];
            int sz = it[0];
            vector<pair<int,int>>factors;
            for(int i=0;i<primes.size() && num>1;i++){
                int count=0;
                while(num%primes[i]==0){
                    num/=primes[i];
                    count++;
                }
                if(count) factors.push_back({primes[i],count});
            }
            long long ans=1;
            for(auto it : factors) ans = (ans*choose[sz+it.second-1][it.second])%mod;
            final.push_back(ans);
        }
        return final;
    }
};
43600