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.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        new Main().run();
    }


    private void run() throws IOException {

        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String[] line = reader.readLine().split("\\s");
        int x = Integer.parseInt(line[0]);
        long n = Long.parseLong(line[1]);
        long mod = 1000000007;

        Set<Integer> primes = getPrimes(x);
        long res = 1;
        for(int p: primes){
            long degree = 0, nCopy = n;
            while (nCopy > 1){
                nCopy = nCopy / ((long) p);
                degree += nCopy;
            }
            boolean[] bits = new boolean[64];
            for (int i = bits.length-1; i >= 0; i--) {
                if(degree % 2 == 1)
                    bits[i] = true;
                degree >>= 1;
            }
            long tmp = 1;
            for (int i = 0; i < bits.length; i++) {
                tmp = (tmp * tmp) % mod;
                if(bits[i])
                    tmp = (tmp * p) % mod;
            }
            res = (res * tmp) % mod;
        }

        System.out.println(res);
    }

    private Set<Integer> getPrimes(int x){

        Set<Integer> primes = new HashSet<>();
        double sqrt = Math.sqrt(x) + 1;
        int multiplier = 2, tmp = x;
        while (x > 1 && multiplier < sqrt){
            if(x % multiplier == 0){
                primes.add(multiplier);
                x /= multiplier;
            }else if(multiplier == 2){
                multiplier++;
            }else{
                multiplier += 2;
            }
        }

        if(x > 1)
            primes.add(x);

        return primes;
    }


}