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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#define mod 1000000007

long long calc(long long a,long long b){
  if(b == 0) return 1;
  if(b%2 == 0){
    long long d = calc(a,b/2);
    return (d*d)%mod;
  }
  return (a*calc(a,b-1))%mod;
}

long long comb(long long n,long long r){
  long long tmp = 1,ttmp = 1;
  for(int i = n;i >= n-r+1;i--) tmp = (tmp*i)%mod;
  for(int i = 1;i <= r;i++) ttmp = (ttmp*i)%mod;
  return (tmp*calc(ttmp,mod-2))%mod;
}

int main(void){
  int N,M;
  scanf("%d%d",&N,&M);

  int insu[100000];
  for(int i = 0;i < 100000;i++) insu[i] = 0;

  int cnt = 0;
  for(int i = 2;i*i <= M;i++){
    if(M%i == 0){
      while(M%i == 0){
        insu[cnt]++;
        M /= i;
      }
      cnt++;
    }
  }
  if(M > 1) insu[cnt]++;

  long long ans = 1;
  for(int i = 0;i <= cnt;i++){
    ans *= comb(insu[i]+N-1,insu[i]);
    ans %= mod;
  }

  printf("%lld\n",ans);

  return 0;
}