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.
/**
 * ******* Created by K1K on 29/9/19 6:29 PM*******
 */

import java.io.*;
import java.util.*;

public class C1228 implements Runnable {
    List<Integer> primes = new ArrayList<>();
    public static final int MAX =(int) (1E5+100);
    public static final int MOD =(int) (1E9+7);
    boolean[] flag = new boolean[MAX];
    private void solve() throws IOException {
        int x = reader.nextInt();
        long n = reader.nextLong();
        sieve();
        for(int i=0;i<MAX;i++)if(!flag[i])primes.add(i);
        List<Integer> p = new ArrayList<>();
        int temp =x;
        for(int i=0;i<primes.size() && temp>0;i++){
            if(temp% primes.get(i)==0){
                while(temp >0 && temp%primes.get(i)==0)temp/=primes.get(i);
                p.add(primes.get(i));
            }
        }
        if(temp>1)p.add(temp);
      //  for(int i=0;i<p.size();i++) System.out.println(p.get(i));
        if(p.size() ==0){
            System.out.println("0");
            return;
        }
        long ans =1;
        for(int i=0;i<p.size();i++){
            long p1 = p.get(i);
            long t =n;
            while(t>0){
                long tem = t/p1;
                long val =power(p.get(i),tem)%MOD;
                ans = (ans * val) %MOD;
                t/=p.get(i);
            }
        }
        System.out.println(ans);
    }

    private long power(long a, long b) {
        long res =1;
        while(b>0){
            if(b%2 ==1)res =(res*a)%MOD;
            a= (a*a)%MOD;
            b/=2;
        }
        return res;
    }

    private void sieve() {
        flag[0] = true;
        flag[1]=true;
        for(int i=2;i*i<MAX;i++){
            if(!flag[i]){
                for(int j=i*i;j<MAX;j+=i){
                    flag[j]=true;
                }
            }
        }
    }

    public static void main(String[] args) throws IOException {
        try (Input reader = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            new C1228().run();
        }
    }

    StandardInput reader;
    PrintWriter writer;

    @Override
    public void run() {
        try {
            reader = new StandardInput();
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    interface Input extends Closeable {
        String next() throws IOException;

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

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

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

        default int[] readIntArray() throws IOException {
            return readIntArray(nextInt());
        }

        default int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        default long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextLong();
            }
            return array;
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }
}
