Let's introduce some definitions that will be needed later.

Let prime(x) be the set of prime divisors of x. For example, prime(140) = \{ 2, 5, 7 \}, prime(169) = \{ 13 \}.

Let g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:

  * g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27), 
  * g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49). 



Let f(x, y) be the product of g(y, p) for all p in prime(x). For example:

  * f(30, 70) = g(70, 2) ⋅ g(70, 3) ⋅ g(70, 5) = 2^1 ⋅ 3^0 ⋅ 5^1 = 10, 
  * f(525, 63) = g(63, 3) ⋅ g(63, 5) ⋅ g(63, 7) = 3^2 ⋅ 5^0 ⋅ 7^1 = 63. 



You have integers x and n. Calculate f(x, 1) ⋅ f(x, 2) ⋅ … ⋅ f(x, n) mod{(10^{9} + 7)}.

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

Output

Print the answer.

Examples

Input


10 2


Output


2


Input


20190929 1605


Output


363165664


Input


947 987654321987654321


Output


593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.
// package Codeforces_Round_589_Div2;

import java.util.*;
import java.lang.*;
import java.io.*;

public class C {
	public static long mod = (long)(1e9+7);
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner fr = new Scanner(System.in);
		int x = fr.nextInt();
		long n = fr.nextLong();
		ArrayList<Integer> prime_factors = findPrimes(x);
		long ans = 1;
		
		for(int val: prime_factors) {
			int prime = val;
			long count = 0;
			long times = n / prime;
			
			while(times > 0) {
				count += times;
				times = times / prime;
			}
			
			count = count % (mod - 1);
			ans = ans * pow(prime, count);
			ans = ans % mod;
		}
		
		ans = ans % mod;
		System.out.println(ans);
		
	}
	
	public static long pow(int base, long exp) {
		if(exp == 0) {
			return 1;
		}
		
		long ans = pow(base, exp / 2);
		ans = ans % mod;
		
		ans = ans * ans;
		ans = ans % mod;
		
		if(exp % 2 == 1) {
			ans = ans * base;
			ans = ans % mod;
		}
		
		return ans;
	}
	
	private static ArrayList<Integer> findPrimes(int x) {
	    ArrayList<Integer> primes = new ArrayList<>();
	 
	    int i = 2;
	    while (i * i <= x) {
	      if (x % i == 0) {
	        primes.add(i);
	 
	        while (x % i == 0) {
	          x /= i;
	        }
	      }
	 
	      i++;
	    }
	 
	    if (x > 1) {
	      primes.add(x);
	    }
	 
	    return primes;
	  }

}
