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: Wrong Answer)

#include <stdio.h>
#include <stdbool.h>


int combination(long n,long m){
	if(n==m || m==0) return 1;
	else return combination(n-1,m-1) + combination(n-1,m);
}

int main(void){
	long n,m;
	scanf("%ld %ld",&n,&m);
	long x,i=0;
	long ans=1;
	long tmp[100]={0};
	for(x=2; m>1; x++){
		while((m%x)==0){
			i++;
			m /= x;
		}
		ans *= combination(n-1+i, i);
    	i=0;
	}
	printf("%ld",ans);
	return 0;

}