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 javafx.util.Pair;

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException{

        Locale.setDefault(Locale.US);
        //----------------CODE HERE-------------------
        int x;
        long n;
        x = sc.nextInt();
        n = sc.nextLong();

        HashMap<Integer, Integer> divisors = new HashMap<>();

        while (x%2==0)
        {
            if(!divisors.containsKey(2)) {
                divisors.put(2,0);
            }
            divisors.put(2, divisors.get(2)+1);
            x /= 2;
        }

        for (int i = 3; i <= Math.sqrt(x); i+= 2)
        {
            while (x%i == 0)
            {
                if(!divisors.containsKey(i)) {
                    divisors.put(i,0);
                }
                divisors.put(i, divisors.get(i)+1);
                x /= i;
            }
        }
        if(x>2) {
            if(!divisors.containsKey(x)) {
                divisors.put(x,0);
            }
            divisors.put(x, divisors.get(x)+1);
        }

        long res = 1;

        for(Map.Entry<Integer,Integer> entry : divisors.entrySet()) {
            long l = entry.getKey();
            long count = 0;
            while (l <= n) {
                count += n/l;
                try {
                    l = Math.multiplyExact(l, entry.getKey());
                } catch(ArithmeticException e) {
                    break;
                }
            }

            res *= power(entry.getKey(), count, 1000000007);
            res %= 1000000007;
        }

        out.println(res);

        //----------------CODE HERE--------------------
        out.flush();
    }

    static long power(long x, long y, int p)
    {
        // Initialize result
        long res = 1;

        // Update x if it is more
        // than or equal to p
        x = x % p;

        while (y > 0)
        {
            // If y is odd, multiply x
            // with result
            if((y & 1)==1)
                res = (res * x) % p;

            // y must be even now
            // y = y / 2
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    //-----------PrintWriter for faster output---------------------------------
    public static MyScanner sc = new MyScanner();
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //--------------------------------------------------------
}
