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.
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
*/
import java.util.*;
import java.io.*;
 
   public class C
   {
      public static void main(String args[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         long X = Long.parseLong(st.nextToken());
         long N = Long.parseLong(st.nextToken());
         //gen prime factors of N
         ArrayList<Integer> pf = findDiv((int)X);
         long[] res = new long[pf.size()];
         for(int i=0; i < pf.size(); i++)
         {
            int prime = pf.get(i);
            int cnt = count(N, prime);
            long val = 1L;
            for(int e=1; e <= cnt; e++)
            {
               val *= prime;
               res[i] += N/val;
               //System.out.println(N/val);
            }
         }
         long rest = 1L;
         long MOD = 1000000007L;
         for(int i=0; i < pf.size(); i++)
         {
            rest *= power(pf.get(i), res[i], MOD);
            rest %= MOD;
         }
         System.out.println(rest);
      }
      public static int count(long N, int x)
      {
         int res = 0;
         while(N/x > 0)
         {
            N /= x;
            res++;
         }
         return res;
      }
      public static ArrayList<Integer> findDiv(int N)
      {
         //gens all divisors of N
         ArrayList<Integer> ls1 = new ArrayList<Integer>();
         ArrayList<Integer> ls2 = new ArrayList<Integer>();
         int sqrt = (int)(Math.sqrt(N));
         int n = N;
         for(int i=2; i <= sqrt; i++)
            if(n%i == 0)
            {
               ls1.add(i);
               while(n%i == 0)
                  n /= i;
            }
         if(n != 1)
            ls1.add(n);
         return ls1;
      }
      public static long power(long x, long y, long p) 
      { 
          long res = 1L;
          x = x % p;  
          while (y > 0) 
          { 
              if((y & 1)==1) 
                  res = (res * x) % p; 
              y = y >> 1;  
              x = (x * x) % p;  
          } 
          return res; 
      }
   }