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.*;
import java.util.*;

public class Main {
    static int inf = (int) 1e9 + 7;
    static long pow(long a, long b) {
        long ans = 1;
        while(b != 0) {
            if ((b & 1) != 0) {
                ans = (ans * a) % inf;
            }
            a = (a * a) % inf;
            b /= 2;
        }

        return ans;
    }
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        int x = nextInt();
        long n = nextLong();
        ArrayList<Integer> var = new ArrayList<>();
        for(int i = 2;i <= Math.sqrt(x);i++) {
            if (x % i == 0) {
                while(x % i == 0) x/= i;
                var.add(i);
            }
        }
        if (x != 1) var.add(x);
        long ans = 1;

        for(long d : var) {
            long v = n;
            long new_d = 1;
            long two = 1;
            while(v != 0) {
                long one = pow(new_d, v - v / d) % inf;
                two = (two * one) % inf;
                new_d = (new_d * d) % inf;
                v /= d;
            }
            ans = (ans * two) % inf;
        }
        pw.println(ans);
        pw.close();
    }

    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");
    static PrintWriter pw;

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

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

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

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