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

public class Main {
    static long mod=1000000007;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long x=sc.nextLong();
        long n=sc.nextLong();
        ArrayList<Long> primes=primeFactors(x);
        long res=1;
        for (long p:primes){
            long pow=0;
            long temp=p;
            while (true){
                pow+=(n/temp);
                if (n/temp<p)break;
                temp*=p;
            }
            res=(res*powMod(p,pow,mod))%mod;
        }
        System.out.println(res);
    }
    static long powMod(long x,long pow,long mod){
        if (pow==0)return 1;
        if (pow%2==0){
            long y=powMod(x,pow/2,mod);
            return ((y%mod)*(y%mod))%mod;
        }
        return ((x%mod)*powMod(x,pow-1,mod))%mod;
    }
    static ArrayList<Long> primeFactors(long x){
        ArrayList<Long> arr=new ArrayList<>();
        for (long i=2;i*i<=x;i++){
            if (x%i==0){
                arr.add(i);
                while (x%i==0){
                    x=x/i;
                }
            }
        }
        if (x>1)arr.add(x);
        return arr;
    }
}