main.cpp

#include <iostream>
#include <bits/stdc++.h>

using namespace std;

int comb[10013][14] = {1}, mod = 1000000007;
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};
class Solution
{
public:
    vector<int> waysToFillArray(vector<vector<int>> &qs)
    {
        if (comb[1][1] == 0)
            for (int n = 1; n < 10013; ++n)
                for (int r = 0; r < 14; ++r)
                    comb[n][r] = r == 0 ? 1 : (comb[n - 1][r - 1] + comb[n - 1][r]) % mod;
        vector<int> res(qs.size(), 1);
        for (auto i = 0; i < qs.size(); ++i)
        {
            int n = qs[i][0], k = qs[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;
    }
};

int main()
{
    Solution s;
    vector<vector<int>> qs;
    vector<int> res;
    qs.push_back({3, 2});
    qs.push_back({2, 2});
    qs.push_back({3, 3});
    qs.push_back({2, 3});
    qs.push_back({3, 4});
    qs.push_back({2, 4});
    qs.push_back({3, 5});
    qs.push_back({2, 5});
    res = s.waysToFillArray(qs);
    for (auto i : res)
        cout << i << " ";
    cout << endl;
    return 0;
}