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.

/**
 * @author egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict Accepted
 * @url <https://codeforces.com/problemset/problem/1228/C>
 * @category maths
 * @date 01/10/2019
 **/

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.StringTokenizer;
import java.util.TreeSet;

import static java.lang.Long.parseLong;

public class CF1228C {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        for (String ln; (ln = in.readLine()) != null; ) {
            StringTokenizer st = new StringTokenizer(ln);
            long X = parseLong(st.nextToken()), N = parseLong(st.nextToken()), sqrt = (long) Math.sqrt(X);
            TreeSet<Long> primes = new TreeSet<>();
            for (long p = 2; p <= sqrt && X > 1; p++)
                if (X % p == 0) {
                    primes.add(p);
                    for (; X % p == 0; )
                        X /= p;
                }
            if (X > 1) primes.add(X);
            long val = 1;
            for(long p:primes) {
                long r=0,n=N;
                for(;n>1;n/=p)r+=n/p;
                val=(val*BigInteger.valueOf(p).modPow(BigInteger.valueOf(r), BigInteger.valueOf(1000000007)).longValue())%1000000007;
            }
            System.out.println(val);
        }
    }
}
