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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());
        int x = Integer.parseInt(st.nextToken());
        long n = Long.parseLong(st.nextToken());
        boolean[] primes = sieve(100000);
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 1; i * i <= x; i++) {
            if (x % i == 0) {
                if (primes[i]) {
                    list.add(i);
                }
            }
            if (x % i == 0 && i * i != x) {
                if (isPrime(x / i)) {
                    list.add(x / i);
                }
            }
        }
        Collections.sort(list);
        long result = 1;
        for (int prime : list) {
            long count = 0;
            for (long check = prime; check > 0 && check <= n; ) {
                count += n / check;
                long test = check;
                check = test * prime;
                if (check / test != prime) {
                    break;
                }
            }
            result = (result * calculatePow(prime, count)) % (1000000007);
        }
        pw.println(result);
        pw.close();
    }

    private static boolean[] sieve(int n) {
        boolean prime[] = new boolean[n + 1];
        for (int i = 2; i < n; i++)
            prime[i] = true;

        for (int p = 2; p * p <= n; p++) {
            // If prime[p] is not changed, then it is a prime
            if (prime[p]) {
                // Update all multiples of p
                for (int i = p * 2; i <= n; i += p)
                    prime[i] = false;
            }
        }
        return prime;
    }

    private static int calculatePow(int num, long pow) {
        if (pow == 0) {
            return 1;
        }
        long res = calculatePow(num, pow / 2);
        res = (res * res) % (1000000007);
        if (pow % 2 == 1) {
            return (int) ((res * num) % (1000000007));
        }
        return (int)res;
    }

    private static boolean isPrime(int num) {
        boolean flag = true;
        for (int i = 2; i * i <= num; i++) {
            if (num % i == 0) {
                flag = false;
                break;
            }
        }
        return flag;
    }
}
