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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class Main {

    static Set<BigInteger> getPrimesDivisors(int n) {
        Set<BigInteger> res = new HashSet<>();
        int sqrt = (int) Math.sqrt(n);
        for (int i = 2; i <= sqrt; ) {
            if (n % i == 0) {
                res.add(BigInteger.valueOf(i));
                n /= i;
                while (n % i == 0) {
                    n /= i;
                }
            } else {
                ++i;
            }
        }
        if (n > 1) {
            res.add(BigInteger.valueOf(n));
        }
        return res;
    }

    public static void main(String[] args) throws Exception {
        try (InputReader reader = new InputReader(System.in)) {
            try (PrintWriter writer = new PrintWriter(System.out)) {
                BigInteger mod = BigInteger.valueOf(1000000007);
                int x = reader.nextInt();
                BigInteger n = BigInteger.valueOf(reader.nextLong());
                Set<BigInteger> primes = getPrimesDivisors(x);
                BigInteger ans = BigInteger.ONE;
                for (BigInteger prime : primes) {
                    BigInteger k = prime;
                    while (n.compareTo(k) >= 0) {
                        ans = ans.multiply(prime.modPow(n.divide(k), mod));
                        ans = ans.mod(mod);
                        k = k.multiply(prime);
                    }
                }
                writer.print(ans.mod(mod));
            }
        }
    }

    static class InputReader implements AutoCloseable {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 1 << 18);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        @Override
        public void close() throws Exception {
            reader.close();
        }
    }
}