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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
public class Main{
	static long mod;
	static long ans;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		long n=sc.nextLong();
		long m=sc.nextLong();
		mod=1000000007;
		ans=1;
		for(long i = 2; i<=m; i++){
			long count=0;
			while(m%i==0){
				m/=i;
				count++;
			}
			if(count>0){
				for(long j=1; j<=count; j++){
					ans*=((n+count-j)%mod);
					ans%=mod;
				}
				for(long k=2; k<=count; k++){
					pow(k,mod-2);
				}
			}
		}
		System.out.println(ans);
	}
	public static void pow(long a,long p){
		while(p>0){
			if((p & 1)==1){
				ans*=a;
				ans%=mod;
			}
			
			a*=a;
			a%=mod;
			p>>=1;
		}
	}
}