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.awt.*;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    //BufferedReader br = new BufferedReader(new FileReader("hall.in"));

    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);
    //PrintWriter pw = new PrintWriter("hall.out");

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

    String next() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

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

    public Main() throws FileNotFoundException {
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    long mod = (long) 1e9 + 7;

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

    void run() throws IOException {
        long x = nextLong();
        long n = nextLong();
        long y = x;
        ArrayList<Long> del = new ArrayList<>();
        while (y > 1) {
            long e = 0;
            for (int i = 2; i <= sqrt(y); i++) {
                if (y % i == 0) {
                    e = i;
                    break;
                }
            }
            if (e != 0) {
                while (y % e == 0) y /= e;
                del.add(e);
            } else {
                del.add(y);
                break;
            }
        }
        long ans = 1;
        for (int i = 0; i < del.size(); i++) {
            long r = del.get(i);
            long max = 1;
            while (max <= (long) 1e18 / r && max * r <= n) max *= r;
            long prev = 0;
            while (max > 1) {
                ans *= pow(max, n / max - prev);
                ans %= mod;
                prev = n / max;
                max /= r;
            }
        }
        pw.println(ans);
        pw.close();
    }

    class Pair {
        int x, y;

        public Pair(int a, int b) {
            x = a;
            y = b;
        }
    }

    class PairComp implements Comparator<Pair> {

        @Override
        public int compare(Pair o1, Pair o2) {
            if (o1.x == o2.x) return Integer.compare(o1.y, o2.y);
            return Integer.compare(o1.x, o2.x);
        }
    }
}