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.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

import static java.lang.Long.parseLong;
import static java.nio.charset.StandardCharsets.UTF_8;

public class Main {

    public static void main(String[] args) throws IOException {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in, UTF_8));
             BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out, UTF_8))) {
            StringTokenizer tokens = new StringTokenizer(in.readLine());
            long x = parseLong(tokens.nextToken());
            long n = parseLong(tokens.nextToken());
            List<long[]> factors = findFactoring(x);
            long[] primes = new long[factors.size()];
            for (int i = 0; i < primes.length; i++) {
                primes[i] = factors.get(i)[0];
            }
            long ans = 1;
            for (int i = 0; i < primes.length; i++) {
                long p = primes[i];
                long deg = 0;
                while (n / p > 0) {
                    deg += n / p;
                    if (Long.MAX_VALUE / primes[i] < p) {
                        break;
                    }
                    p *= primes[i];
                    if (p > n) {
                        break;
                    }
                }
                long mult = deg(primes[i], deg);
                ans = (ans * mult) % 1000000007;
            }
            out.write(ans + "");
            out.newLine();
        }
    }

    private static long deg(long x, long k) {
        if (k == 0) {
            return 1;
        }
        x %= 1000000007;
        if (k % 2 == 1) {
            return (x * deg((x * x) % 1000000007, k / 2)) % 1000000007;
        } else {
            return deg((x * x) % 1000000007, k / 2) % 1000000007;
        }
    }

    private static List<long[]> findFactoring(long b) {
        List<long[]> divs = new ArrayList<>();
        if (BigInteger.valueOf(b).isProbablePrime(100)) {
            divs.add(new long[]{b, 1});
            return divs;
        }
        for (long i = 2; i <= b; i++) {
            if (b % i == 0) {
                int deg = 0;
                while (b % i == 0) {
                    deg++;
                    b /= i;
                }
                divs.add(new long[]{i, deg});
                if (BigInteger.valueOf(b).isProbablePrime(100)) {
                    divs.add(new long[]{b, 1});
                    return divs;
                }
            }
        }
        return divs;
    }
}
