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.util.*;
import java.lang.*;
// StringBuilder uses java.lang
 
 
public class mainClass {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        ArrayList<Integer> listOfPrimes = new ArrayList<>();
        int r = n*1;
        for (int i=2;i<=Math.sqrt(n);i++) {
            if (r == 1) {
                break;
            }
            if (r % i == 0) {
                listOfPrimes.add(i);
            }
            int t = 0;
            while(r % i == 0) {
                t+=1;
                r/=i;
            }
        }
        if (r>1) {
            listOfPrimes.add(r);
        }
        long g = sc.nextLong();
        long ans = 1;
        for (int i=0;i<listOfPrimes.size();i++) {
            if (listOfPrimes.get(i)>g) {
                break;
            }
            long l = listOfPrimes.get(i);
            for (int j=1;j<62;j++) {
                long ok = g/l;
                ans*=fastPow(listOfPrimes.get(i),(ok % 1000000006),1000000007);
                ans%=1000000007;
                if (g/listOfPrimes.get(i)<l) {
                    break;
                }
                l*=listOfPrimes.get(i);
            }
        }
        System.out.println((ans+1000000007)%1000000007);
    }
    public static long fastPow(int base,long exp,int mod) {
        if (exp==0) {
            return 1;
        } else {
            if (exp % 2 == 1) {
                long z = fastPow(base,(exp-1)/2,mod);
                return ((((z*base) % mod) * z) % mod);
            } else {
                long z = fastPow(base,exp/2,mod);
                return ((z*z) % mod);
            }
        }
    }
}