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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Solve7 {

    public static void main(String[] args) throws IOException {
        PrintWriter pw = new PrintWriter(System.out);
        new Solve7().solve(pw);
        pw.flush();
        pw.close();
    }

    public void solve(PrintWriter pw) throws IOException {
        FastReader sc = new FastReader();
        long x = sc.nextLong(), n = sc.nextLong();
        ArrayList<Long> a = new ArrayList();
        if ((x & 1) == 0) {
            a.add(2l);
            while ((x & 1) == 0) {
                x >>= 1;
            }
        }
        for (long j = 3; j * j <= x; j += 2) {
            if (x % j == 0) {
                a.add(j);
                while (x % j == 0) {
                    x /= j;
                }
            }
        }
        if (x > 1) {
            a.add(x);
        }
        final int MOD = (int) 1E+9 + 7;
        long s = 1;
        for (int i = 0; i < a.size(); i++) {
            long p = a.get(i);
            long[] freq = new long[61];
            for (int j = 1; j <= 60; j++) {
                long temp = power(p, j, n);
                if (temp == -1) {
                    break;
                }
                long y = (long) n / temp;
                freq[j] = y;
                freq[j - 1] -= y;
            }
            for (int j = 1; j <= 60; j++) {
                if (freq[j] == 0) {
                    break;
                }
                s = (s * (powerWithMod(powerWithMod(p, j, MOD), freq[j], MOD)) % MOD) % MOD;
            }
        }
        pw.println(s);
    }

    public long powerWithMod(long a, long n, long mod) {
        if (n == 0) {
            return 1;
        }
        long y = powerWithMod(a, n / 2, mod);
        if ((n & 1) == 1) {
            return (((y * y) % mod) * a) % mod;
        } else {
            return (y * y) % mod;
        }
    }

    public long power(long a, int n, long f) {
        BigInteger x = BigInteger.ONE;
        for (int i = 0; i < n; i++) {
            x = x.multiply(BigInteger.valueOf(a));
            if (x.compareTo(BigInteger.valueOf(f)) > 0) {
                return -1;
            }
        }
        return x.longValue();
    }

    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
            }
        }

        public String next() {
            if (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
            }
            return st.nextToken();
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
            }
            return null;
        }

        public boolean hasNext() throws IOException {
            if (st != null && st.hasMoreTokens()) {
                return true;
            }
            String s = br.readLine();
            if (s == null || s.isEmpty()) {
                return false;
            }
            st = new StringTokenizer(s);
            return true;
        }
    }
}
