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 A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String s1[]=br.readLine().split(" ");
            int x=Integer.parseInt(s1[0]);
            long n=Long.parseLong(s1[1]);
            
            ArrayList<Integer> al=new ArrayList<Integer>();
            int y=x;
            for(int i=2;i<=Math.sqrt(x);i++)
            {
                  if(y%i!=0)
                   continue;
                  al.add(i);
                  while(y%i==0)
                  {
                        y=y/i;
                        
                  }
            }
            
            if(y>=2)
             al.add(y);
            
            // System.out.println(al);
            long t=1;
            long mod=1000000007;
            for(int i=0;i<al.size();i++)
            {
                  t=(t*g(n,(long)al.get(i)))%mod;
            }
            
            System.out.println(t);
      }
      
      public static long g(long n,long p)
      {
            long t=0;
            long r=p;
            while(n>0)
            {
                  t+=n/p;
                  n=n/p;
                  // r=r*p;
            }
            // System.out.println(p+" "+t);
            return pow(p,t);
      }
      
      public static long pow(long x,long n)
      {
            long mod=1000000007;
            long r=1;
            while(n>0)
            {
                  if(n%2==1)
                   r=(r*x)%mod;
                  x=(x*x)%mod;
                  n=n/2;
            }
            return r;
      }
}