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 test2 {

    static ArrayList<Long> primeFactors(long n)
    {
        LinkedHashSet<Long> set = new LinkedHashSet<>();
        while (n%2==0) {
            set.add((long)2);
            n /= 2;
        }

        for (long i = 3; i <= Math.sqrt(n); i+= 2) {
            while (n%i == 0) {
                set.add(i);
                n /= i;
            }
        }

        if (n > 2)
            set.add(n);
        return new ArrayList<>(set);
    }


    public static void main(String args[]) throws IOException
    {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] xn = br.readLine().trim().split(" ");
        long x = Long.parseLong(xn[0]);
        long n = Long.parseLong(xn[1]);
        ArrayList<Long> p = primeFactors(x);
        System.out.print(answ(p,n));
    }

    static long answ(ArrayList<Long> p,long n){
        long ans=1;
        for(Long l : p){
            long c=0;
            long i = n;
            while (i>=l){
                c = c +i/l;
                i = i/l;
            }
            ans = (ans * po(l,c))%1000000007;
        }
        return ans;
    }

    static long po(long a, long b){
        long ans = 1;
        while (b>0){
            if((b&1) >0)
                ans = (ans*a)%1000000007;
            a = (a*a)%1000000007;
            b = b>>1;
        }
        return ans;
    }
}