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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
typedef long long int int64;
const int mod=1000000007;
int comb(int n,int k){
  int res=1;
  int inv[31];
  inv[1]=1;
  int i;
  for(i=1;i<=k;i++){
    if(i>=2) inv[i]=mod-(int64)(mod/i)*inv[mod%i]%mod;
    res=(int64)res*(n+1-i)%mod*inv[i]%mod;
  }
  return res;
}
void run(void){
  int n,m;
  scanf("%d%d",&n,&m);
  int ans=1;
  int k;
  for(k=2;k*k<=m;k++){
    if(m%k==0){
      int c=0;
      while(m%k==0){
	c++;
	m/=k;
      }
      ans=(int64)ans*comb(n-1+c,c)%mod;
    }
  }
  if(m>1) ans=(int64)ans*comb(n-1+1,1)%mod;
  printf("%d\n",ans);
}
int main(void){
  run();
  return 0;
}