Problem:
Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <iomanip>
#include <algorithm>
#include <cmath>
#define REP(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 60;
constexpr int MAX = 100010;
long fac[MAX], inv[MAX], finv[MAX];
void init()
{
    fac[0] = inv[0] = finv[0] = 1;
    fac[1] = inv[1] = finv[1] = 1;
    for (int i = 2; i < MAX; ++i)
    {
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
// 区別できるnこの中からkこ選ぶときの組み合わせの総数
long C(int n, int k)
{
    if (n < 0 || k < 0 || n < k)
        return 0;
    return (fac[n] * finv[n - k] % MOD) * finv[k] % MOD;
}
// 区別できるnこの中から重複を許してkこ選ぶときの組み合わせの総数
long H(int n, int k)
{
    return C(n + k - 1, k);
}

ll n, m;

int main()
{
  cin >> n >> m;
  init();
  ll ans = 1;
  for(ll i = 2; i * i <= m; ++i) {
    ll cnt = 0;
    while (m % i == 0) {
      m /= i;
      ++cnt;
    }
    ans = ans * H(n, cnt) % MOD;
  }
  if (m != 1) {
    ans = ans * n % MOD;
  }
  cout << ans;
  return 0;
}