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.util.StringTokenizer;

public class PrimesAndMultiplication {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer tokenizer = new StringTokenizer(f.readLine());
        int x = Integer.parseInt(tokenizer.nextToken());
        long n = Long.parseLong(tokenizer.nextToken());
        int mod = 1000000007;
        long result = 1;
        for (int i = 1; i * i <= x; i++) {
            if (x % i == 0 && isPrime(i)) {
                long value = 1;
                while (n / i >= value) {
                    value *= i;
                }

                long picked = 0;
                while (value > 1) {
                    result *= getNumPowerMod(value % mod, (n / value - picked), mod);
                    result %= mod;
                    /*
                    for (int k = 0; k < n / value - picked; k++) {
                        System.out.println("wop " + " " + (n / value - picked));
                        result *= value;
                        result %= mod;
                    } */

                    picked += n / value - picked;
                    value /= i;
                }
            }

            int oldI = i;
            i = x / i;
            if (oldI != i && x % i == 0 && isPrime(i)) {
                long value = 1;
                while (n / i >= value) {
                    value *= i;
                }


                long picked = 0;
                while (value > 1) {
                    result *= getNumPowerMod(value % mod, (n / value - picked), mod);
                    result %= mod;
                    /*
                    for (int k = 0; k < n / value - picked; k++) {
                        System.out.println("wop " + " " + (n / value - picked));
                        result *= value;
                        result %= mod;
                    } */

                    picked += n / value - picked;
                    value /= i;
                }
            }
            i = oldI;
        }

        System.out.println(result);
    }

    private static boolean isPrime(int n) {
        if (n == 1) {
            return false;
        }
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                return false;
            }
        }

        return true;
    }

    private static long getNumPowerMod(long a, long b, int mod) {
        long res = 1;
        while (b > 0) {
            if ((b & 1) == 1) {
                res *= a;
                res %= mod;
                b--;
            } else {
                a *= a;
                a %= mod;
                b /= 2;
            }
        }

        return res;
    }

}
