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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        static final int MOD = (int) (1e9 + 7);

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int x = in.nextInt();
            long n = in.nextLong();
            HashSet<Integer> primeFactorize = primeFactors(x);
            long res = 1;
            for (long val : primeFactorize) {
                long tempval = val;
                int counter = 1;
                while (tempval <= n && tempval > 0) {
                    long value = (n / tempval);
                    res *= modularEx(val, value);
                    res %= MOD;
                    if (n / tempval < val) {
                        break;
                    }
                    tempval *= val;
                    counter++;
                }
            }
            out.println(res);
        }

        public static long modularEx(long b, long p) {
            long res = 1;
            b %= MOD;
            while (p > 0) {
                if ((p & 1) == 1) {
                    res *= b;
                    res %= MOD;
                }
                p /= 2;
                b *= b;
                b %= MOD;
            }
            return res % MOD;
        }

        public static HashSet<Integer> primeFactors(int n) {
            HashSet<Integer> primeFactors = new HashSet<>();
            while (n % 2 == 0) {
                primeFactors.add(2);
                n /= 2;
            }

            // n must be odd at this point.  So we can
            // skip one element (Note i = i +2)
            for (int i = 3; i <= Math.sqrt(n); i += 2) {
                // While i divides n, print i and divide n
                while (n % i == 0) {
                    primeFactors.add(i);
                    n /= i;
                }
            }

            // This condition is to handle the case whien
            // n is a prime number greater than 2
            if (n > 2) {
                primeFactors.add(n);
            }
            return primeFactors;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

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

    }
}

