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.io.*;
import java.util.*;
public class Solution {
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	//Main Method
	static long MOD=1000000000+7;
	static long exp(long a,long b) {
		if(b==0L) return 1L;
		if((b&1L)==0L) return exp((a*a)%MOD,b/2L)%MOD;
		else return ((a%MOD)*(exp((a*a)%MOD,b/2L)%MOD))%MOD;
	}
	public static void main(String args[]) {
		int test=1;
		while(test-->0) {
			long x=sc.nextLong(),n=sc.nextLong();
			ArrayList<Long> a=new ArrayList<>();
			for(long i=2;i*i<=x;i++) {
				if(x%i==0) a.add(i);
				while(x%i==0) x/=i;
			}
			if(x>1) a.add(x);
			long ans=1L;
			for(long p: a) {
				long val=0L;
				long num=p;
				while(num<=n) {
					val+=n/num;
					if(num>n/p) break;
					num*=p;
				}
				val=exp(p,val);
				ans=((ans%MOD)*(val%MOD))%MOD;
			}
			out.println(ans);
		}
		out.flush();
		out.close();
	}
}
