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.InputMismatchException;
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;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        long mod = (long) 1e9 + 7;

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            long x = in.nextLong();
            long n = in.nextLong();
            int sieve[] = in.sieve(1000000);
            long xx = x;
            HashSet<Long> prime = new HashSet();
            for (int i = 2; i < sieve.length; i++) {
                if (sieve[i] == i) {
                    while (xx % i == 0) {
                        prime.add((long) i);
                        xx = xx / i;
                    }
                }
            }
            if (xx != 1) {
                prime.add(xx);
            }
            ArrayList<Long> list = new ArrayList<>();
            for (long val : prime) {
                list.add(val);
            }
            //System.out.println(list);
            long ans = 1;
            // System.out.println(n);
            for (long pr : list) {
                long cnt = 0;
                long pri = pr;
                while (true) {
                    if (n / pri != 0) {
                        cnt = n / pri;
                        // System.out.println(pri);
                        ans = ans * pow(pr, cnt);
                        ans %= mod;
                        if ((n + pr + 1) / pr < pri) {
                            break;
                        }
                        pri = pr * pri;
                    } else {
                        break;
                    }
                }
                ans %= mod;
            }
            out.println(ans);
        }

        long pow(long a, long b) {
            if (b == 0) {
                return 1;
            }
            if (b % 2 == 0) {
                long val = pow(a, b / 2);
                return (val * val) % mod;
            }
            return (a * pow(a, b - 1)) % mod;
        }

    }

    static class FastReader {
        private final byte[] buf = new byte[8192];
        private final InputStream stream;
        private int curChar;
        private int snumChars;

        public FastReader(InputStream st) {
            this.stream = st;
        }

        public int read() {
            //*-*------clare------

            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] sieve(int n) {
            int ar[] = new int[n + 1];
            ar[0] = 0;
            ar[1] = 1;
            for (int i = 2; i < ar.length; i++) {
                if (ar[i] == 0) {
                    for (int k = i; k < ar.length; k = k + i) {
                        if (ar[k] == 0) {
                            ar[k] = i;
                        }
                    }
                }
            }
            return ar;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

