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: Runtime Error)

import java.util.ArrayList;
import java.util.Scanner;

class Main{
	static final long MOD = 1000000007;


	static long pow=1000000007;




	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		long N = sc.nextLong();
		long M = sc.nextLong();

		ArrayList<Integer> sosu = new ArrayList<Integer>();
		for(int i = 2;i*i <= M;i++){
			boolean flag = true;
			for(int j = 2;j*j<=i;j++){
				if(i%j==0){
					flag = false;
					break;
				}
			}
			if(flag){
				sosu.add(i);
			}
		}
		
		
		ArrayList<Integer> numdata = new ArrayList<Integer>();			//各素数ごとの個数を記録
		int c = 0;
		while(M!=1){
			int scount = 0;		
			while(M%sosu.get(c) == 0){
				scount++;
				M /= sosu.get(c);
			}
			if(scount!=0){
				numdata.add(scount);
			}
			c++;
		}
		long ans = 1;
		
		for(int i = 0;i <numdata.size();i++){
			ans *=comb(numdata.get(i)+N-1,numdata.get(i));
			ans %= pow;
		}
		System.out.println(ans);




	}

	static long comb(long x,Integer y){
		long ue = 1;
		long sita = 1;
		for(int i= 0;i < y;i++){
			ue *= x-i;
			ue %= pow;
			sita *= i+1;
			sita %=pow;
			
		}
		

		long ans = ue*modpow(sita,pow-2)%pow;
		return ans;
	}
	static long modpow(long a,long p){
		if(p == 0){
			return 1;
		}
		if(p % 2 == 0){
			long halfp = p/2;
			long half = modpow(a, halfp);
			return half*half%pow;
		}else{
			return a*modpow(a, p-1)%pow;
		}
	}
}







class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return end - otherpair.end;
	}
}