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.*;

public class r589c {
	static final int MOD=1000000007;
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int x=scan.nextInt();
		long n=scan.nextLong();
		ArrayList<Integer> set=new ArrayList<>();
		for(int i=2;i*i<=x;i++) {
			if(x%i==0) {
				set.add(i);
				while(x%i==0) x/=i;
			}
		}
		if(x>1) set.add(x);
		long res=1L;
		for(int i=0;i<set.size();i++) {
			int fac=set.get(i);
			long ct=0;
			for(int j=1;;j++) {
				long add=n/pow(fac,j);
				ct+=add;
				if(add==0) break;
				if(n/fac<pow(fac,j)) break;
			}
			//			System.out.println(fac+" "+ct);
//						System.out.println(pow(fac,ct));
			res=(res*powmod(fac,ct))%MOD;
		}
		System.out.println(res);
	}
	public static long pow(long i, long j) {
		long res=1L;
		for(int a=0;a<j;a++) res*=i;
		return res;
	}
	public static long powmod(long i, long j) {
		if(j==0) return 1L;
		if(j%2==0) {
			long temp=powmod(i,j/2);
			return (temp*temp)%MOD;
		}
		return (i*powmod(i,j-1))%MOD;
	}
}