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.ArrayList;
import java.util.HashSet;
import java.util.Set;

public class C589 {
    static long modulo = 1000000007;
    public static void main(String[] args) throws IOException {
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        String[] s1 = inp.readLine().split(" ");
        long a = Long.parseLong(s1[0]);
        long b = Long.parseLong(s1[1]);

        ArrayList<Long> primes = new ArrayList<>();
        ArrayList<Long> fact = new ArrayList<>();
        long c = (long) Math.sqrt(a);
        for(int i=2;i<=c;i++){
            if(a%i==0){
                if(checkPrime(i)){
                    fact.add((long)i);
                }
                if(Math.pow(i,2)!=a) {
                    if (checkPrime(a / i)) {
                        fact.add(a / i);
                    }
                }
            }
        }
        if(checkPrime(a)){
            fact.add(a);
        }

long multi = 0;
        long ans = 1;
       // System.out.println(fact);
        for(int i=0;i<fact.size();i++){


            long t =  fact.get(i);
            multi = t;
            long count = 0;
            while (t<=b){
                count+=b/t;

                if(t>t*multi){
                    break;
                }
                t = t*multi;
               // System.out.println(t+" "+multi);
            }
            //System.out.println(count);
            ans = (ans*power(multi,count))%modulo;

        }

        //System.out.println(power(2,2));


        System.out.println(ans%modulo);


    }
    static long power(long a,long b){
        if(b==0){
            return 1;
        }
        //int count = 0;
        long ans = a;
        ArrayList<Long> list = new ArrayList<>();

        while (b>1){
            if(b%2==0){
                b = b/2;
                ans = ans%modulo;
                ans = (ans*ans)%modulo;
            }
            else{
                ans = ans%modulo;
                list.add(ans);
                b = b/2;
                ans = (ans*ans)%modulo;
            }
        }
        ans = ans%modulo;
        for(int i=0;i<list.size();i++){
            ans = (list.get(i)*ans)%modulo;
        }
        //System.out.println(ans);
        return ans%modulo;
    }
    static boolean checkPrime(long a){
        int c =(int) Math.sqrt(a);
        for(int i=2;i<=c;i++){
            if(a%i==0){
                return false;
            }
        }
        return true;
    }
}
