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.List;
import java.util.Scanner;

public class CodeforcesC {
    static long M = 1000000007;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int x = scanner.nextInt();
        long n = scanner.nextLong();
        List<Integer> primes = getPrimes(x);
        long result = 1;
        for (Integer p : primes) {
            long power = 0;
            long nn=n;
            while (nn > 1) {
                power += nn / p;
                nn /= p;
            }
            long pwr = p;
            while (power > 0) {
                if ((power & 1) != 0) {
                    result = result * pwr % M;
                }
                pwr = pwr * pwr % M;
                power /= 2;
            }
        }
        System.out.println(result);
    }

    private static List<Integer> getPrimes(int x) {
        List<Integer> primes = new ArrayList<>();
        List<Integer> result = new ArrayList<>();
        primes.add(2);
        if (x % 2 == 0) {
            result.add(2);
            while (x % 2 == 0) x /= 2;
        }
        for (int i = 3; i * i <= x; i += 2) {
            boolean isPrime = true;
            for (Integer p : primes) {
                if (i % p == 0) {
                    isPrime = false;
                    break;
                }
            }
            if (isPrime) {
                primes.add(i);
                if (x % i == 0) {
                    result.add(i);
                    while (x % i == 0) x /= i;
                }
            }
        }
        if (x>1 && !result.contains(x)) result.add(x);
        return result;
    }
}
