<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>

typedef long long ll;
const ll p = 1e9+7;
const ll MX = 2e4;
class Solution {
public:
    vector<ll> generate_primes(){
        vector<ll> res;
        for(int i=2;i<=100;i++){
            int f=1;
            for(int j=2;j<=sqrt(i);j+=1){
                if(i%j==0) f=0;
            }
            if(f) res.push_back(i);
        }
        return res;
    }
    ll inv[MX],fact[MX],invfact[MX];

    void populate(){
        fact[0] = 1;
        for(ll i=1;i<MX;i++){
            fact[i]=fact[i-1]*i;
            fact[i]%=p;
        }
        inv[1] = 1;
        for (ll i=2; i< MX; ++i)
	        inv[i] = (p - (p/i) * inv[p%i] % p) % p;
        invfact[0] = 1;
        for(ll i=1;i<MX;i++){
            invfact[i]=invfact[i-1]*inv[i];
            invfact[i]%=p;
        }
    }


    vector<int> waysToFillArray(vector<vector<int>>& queries) {
        auto primes = generate_primes();
        populate();

        vector<int> ans; //stores the result
        for(auto g:queries){
            ll k=g[0],n=g[1],res=1;
            for(auto prime:primes){
                ll cnt = 0;
                while(n%prime==0){
                    cnt++;
                    n/=prime;
                }
                if(cnt)
                    (((((res*=fact[cnt+k-1])%=p)*=invfact[cnt])%=p)*=invfact[k-1])%=p;
            }
            if(n!=1){
                (res*=k)%=p;
            }
            ans.push_back(res);
        }
        return ans;
    }
};
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