<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 {
    static constexpr int MOD = 1e9+7;
    static constexpr int MAX_N = 2e4+13;
    long long fac[MAX_N], inv[MAX_N];
public:
    long long nCk(int n, int k)
    {
        if(k<0 || k>n) return 0;
        return fac[n]*inv[k]%MOD*inv[n-k]%MOD;
    }
    long long powmod(long long x, int y)
    {
        long long r=1;
        while(y){
            if(y&1)(r*=x)%=MOD;
            (x*=x)%=MOD;
            y>>=1;
        }
        return r;
    }
    map<int, int> pf(int x)
    {
        map<int,int> res;
        for(long long i=2;i*i<=x;++i){
            if(x % i == 0){
                int c = 0;
                while(x % i == 0){
                    c++;
                    x/=i;
                }
                res[i]=c;
            }
        }
        if(x!=1)res[x]=1;
        return res;
    }
    vector<int> waysToFillArray(vector<vector<int>>& queries) {
        fac[0]=1;for(int i=1;i<MAX_N;++i)fac[i]=1LL*i*fac[i-1]%MOD;
        inv[MAX_N-1]=powmod(fac[MAX_N-1],MOD-2);
        for(int i=MAX_N-2;i>=0;--i)inv[i]=1LL*(i+1)*inv[i+1]%MOD;

        vector<int> ans;
        for(const auto& q : queries){
            auto n = q[0], k = q[1];
            auto res = pf(k);
            long long r = 1;
            for(auto& p : res) (r *= nCk(p.second+n-1, p.second))%=MOD;
            ans.push_back(r);
        }
        return ans;
    }
};
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