<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>

using LL = long long;
class Solution {
    LL comb[10015][15]; 
public:
    vector<int> waysToFillArray(vector<vector<int>>& queries) {
        /*
            k ball split to n group ways = C(n+k-1, k)
        */
        int mod = 1e9+7;
        int max_element = 0;
        for(auto& query: queries){
            max_element = max(max_element, query[1]);
        }

        for(int i=0; i<10015; i++){
            comb[i][0] = 1;
            for(int j=1; j<=min(i, 14); j++){
                comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % mod;
            }
        }

        vector<int> res;
        auto primes = get_primes(max_element);
        for(auto& query: queries){
            int gruop = query[0];
            int num = query[1];

            LL ans = 1;
            for(auto& prime: primes){
                if(num%prime!=0) continue;
                if(num<prime) break;

                int cnt = 0;
                while(num%prime==0){
                    cnt++;
                    num/=prime;
                }
                ans = ans*comb[gruop+cnt-1][cnt]%mod;
            }
            res.push_back(ans);
        }
        return res;
    }

    vector<int> get_primes(const int num){
        bool is_prime[num+1];
        memset(is_prime, true, sizeof(is_prime));
        for(int i=2; i*i<=num; i++){
            if(!is_prime[i]) continue;

            for(int j=i*2; j<=num; j+=i) is_prime[j] = false;
        }

        vector<int> primes;
        for(int i=2; i<=num; i++) if(is_prime[i]) primes.push_back(i);
        return primes;
    }
};
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