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 _1228c_primesAndMultiplications {
	static ArrayList<Integer>primes=new ArrayList<>();
	static int mod=(int)1e9+7;
	public static void main(String[] args) throws IOException {
		BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out=new PrintWriter(System.out);
		String str=br.readLine();
		StringTokenizer st=new StringTokenizer(str);
		int x=Integer.parseInt(st.nextToken());
		long n=Long.parseLong(st.nextToken());
		factors(x);
		long ans=1;
		for(int p:primes) {
			long exp=exponent(p,n);
			ans=(ans*power(p,exp))%mod;
//			System.out.println(p+" "+ans+" "+exp);
		}
		out.println(ans);
		out.close();
	}
	public static void factors(int n) {
		for(int i=2;i<=Math.sqrt(n);i++) {
			if(n%i==0) {
				primes.add(i);
				while(n%i==0)
					n/=i;
			}
		}
		if(n!=1)
			primes.add(n);
	}
	public static long exponent(int p,long n) {
		long ans=0;
		while(n!=0) {
			ans+=n/p;
			n/=p;
		}
		return ans;
	}
	
	public static long power(long n,long pow)
	{
		long ans=1L;
		while(pow!=0) {
			if((pow&1)==1)
				ans=(ans*n)%mod;
			
				n=(n*n)%mod;
				pow>>=1;
		}
		return ans%mod;
	}
}
