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

public class Solution{

	public static Integer INT(String s){
		return Integer.parseInt(s);
	}

	public static Long LONG(String s){
		return Long.parseLong(s);
	}

	//==================================================================================================================================================


	public static ArrayList<Integer> sieve(int x) {

		int n=100000;

		boolean prime[]=new boolean[n];
		Arrays.fill(prime, true);

		for(int i=2; i<n; i++)
			if(prime[i]) {
				for(int j=i+i; j<n; j+=i)
					prime[j]=false;
			}

		ArrayList<Integer> list=new ArrayList<>();

		for(int i=2; i<n; i++)
			if(x%i!=0)
				continue;
			else {
				while(x%i==0)
					x/=i;
				list.add(i);
			}

		if(x!=1)
			list.add(x);
		return list;
	}

	static long rst, mod;

	public static void main(String args[]) throws IOException {

		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));	Scanner in=new Scanner(System.in); StringBuilder out=new StringBuilder();
		
		int x=in.nextInt();
		long n=in.nextLong();

		ArrayList<Integer> p=sieve(x);
		
		rst=1L;
		mod=1_000_000_007L;

		for(long item: p) {
			long temp=n/item;
			while(temp!=0) {
				rst=(rst*solve(item, temp))%mod;
				temp/=item;
			}
		}

		System.out.println(rst);
	}

	public static long solve(long item, long cnt) {

		if(cnt==0)
			return 1L;

		if(cnt%2==0)
			return solve((item*item)%mod, cnt/2L)%mod;
		else
			return (item*solve((item*item)%mod, cnt/2L)%mod)%mod;
	}

}