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: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
typedef long long ll;
ll modinv(ll a, ll m) {
  long long b = m, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0)
    u += m;
  return u;
}
int main() {
  ll n, m, s, M = 0, Mod = 1e9 + 7;
  cin >> n >> m;
  map<ll, ll> mp;
  while (m % 2 == 0) {
    M = max(M, ++mp[2]);
    m /= 2;
  }
  s = sqrt(m);
  for (ll j = 3; j <= s; j += 2) {
    while (m % j == 0) {
      M = max(M, ++mp[j]);
      m /= j;
    }
  }
  if (m != 1)
    M = max(M, ++mp[m]);
  ll c[n + M + 1];
  rep(i,n)
    c[i] = 1;
  c[n] = n;
  for (int i = n + 1; i < n + M + 1; i++) {
    c[i] = c[i - 1] * modinv((i - n + 1), Mod) % Mod * i % Mod;
  }
  ll ans = 1;
  for (auto i : mp) {
    ans = ans * c[i.second + n - 1] % Mod;
  }
  cout << ans;
  return 0;
}