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.io.IOException;
import java.util.ArrayList;
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 {
        final long MOD = 1000000007L;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long x = in.nextLong();
            long n = in.nextLong();

            ArrayList<Integer> primes = new ArrayList<>();
            long d = x;
            for (int i = 2; i < Math.sqrt(x) + 1; i++) {
                if (d % i == 0) {
                    primes.add(i);
                    while (d % i == 0)
                        d /= i;
                }
            }
            if (d != 1)
                primes.add((int) d);

            long ans = 1;
            for (int p : primes) {
                long pp = p;
                while (n / pp > 0) {
                    long k = n / pp;
                    ans = (ans * binpow(p, k)) % MOD;
                    if (1.0 * pp * p > n) {
                        break;
                    }
                    pp *= p;
                }
            }
            out.println(ans);
        }

        long binpow(long a, long n) {
            long res = 1;
            while (n != 0) {
                if ((n & 1) == 1)
                    res = (res * a) % MOD;
                a = (a * a) % MOD;
                n >>= 1;
            }
            return res;
        }

    }

    static class InputReader {
        final InputStream is;
        final byte[] buffer = new byte[1024];
        int curCharIdx;
        int nChars;

        public InputReader(InputStream is) {
            this.is = is;
        }

        public int read() {
            if (curCharIdx >= nChars) {
                try {
                    curCharIdx = 0;
                    nChars = is.read(buffer);
                    if (nChars == -1)
                        return -1;
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return buffer[curCharIdx++];
        }

        public long nextLong() {
            int sign = 1;
            int c = skipDelims();
            if (c == '-') {
                sign = -1;
                c = read();
                if (isDelim(c))
                    throw new RuntimeException("Incorrect format");
            }
            long val = 0;
            while (c != -1 && !isDelim(c)) {
                if (!isDigit(c))
                    throw new RuntimeException("Incorrect format");
                val = 10L * val + (c - '0');
                c = read();
            }
            return val * sign;
        }

        private final int skipDelims() {
            int c = read();
            while (isDelim(c)) {
                c = read();
            }
            return c;
        }

        private static boolean isDelim(final int c) {
            return c == ' ' ||
                    c == '\n' ||
                    c == '\t' ||
                    c == '\r' ||
                    c == '\f';
        }

        private static boolean isDigit(final int c) {
            return '0' <= c && c <= '9';
        }

    }
}

