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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		long m=1000000007;
		
		long x=s.nextLong();
		long n=s.nextLong();
		
		boolean[] prime=new boolean[500001];
		
		seive(prime,500000);
		
		ArrayList<Long> list=new ArrayList<>();
		
		for(long i=2;i<=500000;i++)
		{
			if(prime[(int)i]&&x%i==0)
			{
				list.add(i);
				
				while(x%i==0)
				{
					x=x/i;
				}
			}
		}
		
		if(x!=1)
		list.add(x);
		
		//System.out.println(list);
		
		long ans=1;
		
		
		
		for(int i=0;i<list.size();i++)
		{
			long count=0;
			
			for(long j=list.get(i);j<=n;j=j*list.get(i))
			{
				count=count+(n/j);
				if(Long.MAX_VALUE/j<list.get(i))
					break;
			}
			
			ans=(ans%m*power(list.get(i),count,m))%m;
			
		}
		
		System.out.println(ans);
		
	}
	
	public static long power(long a,long b,long m)
	{
		long res=1;
		
		while(b>0)
		{
			if(b%2!=0)
			{
				res=(res%m*a%m)%m;
			}
			
			b=b/2;
			a=(a%m*a%m)%m;
		}
		
		return res;
	}
	
	public static void seive(boolean[] prime,int n)
	{
		Arrays.fill(prime,true);
		
		prime[0]=false;
		prime[1]=false;
		
		for(int i=2;i<=Math.sqrt(n);i++)
		{
			if(prime[i])
			{
				for(int j=i*i;j<=n;j=j+i)
				{
					prime[j]=false;
				}
			}
		}
	}
	
}