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.*;
import java.math.*;

public class C {

	public void realMain() throws Exception {

		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in), 1000000);

		String in = fin.readLine();

		String[] ar = in.split(" ");

		BigInteger x = new BigInteger(ar[0]);
		BigInteger n = new BigInteger(ar[1]);
		
		ArrayList<BigInteger> primes = new ArrayList<BigInteger>();

		for(BigInteger i = new BigInteger("2"); i.multiply(i).compareTo(x) <= 0; i = i.add(BigInteger.ONE)) {
			if(x.mod(i).compareTo(BigInteger.ZERO) == 0) {
				if(!primes.contains(i)) {
					primes.add(i);

				}
				
				
				x = x.divide(i);
				//System.out.println("add " + i + "; new x = " + x);
				i = i.subtract(BigInteger.ONE);
				
			}
		}

		if(x.compareTo(BigInteger.ONE) != 0 && !primes.contains(x)) {
			primes.add(x);
		}

		//System.out.println(primes);

		BigInteger magic = new BigInteger("1000000007");
		BigInteger ans = new BigInteger("1");

		for(BigInteger prime : primes) {
			BigInteger tmp = prime;
			while(tmp.compareTo(n) <= 0) {
				//ans = ans.multiply(tmp).mod(magic);
				tmp = tmp.multiply(prime);
			}

			tmp = tmp.divide(prime);
			BigInteger count = BigInteger.ZERO;
			while(tmp.compareTo(BigInteger.ONE) != 0) {
				BigInteger tmp2 = n.divide(tmp);

				ans = ans.multiply(tmp.modPow(tmp2.subtract(count), magic)).mod(magic);
				
				
				//System.out.println("adding " + tmp + "^" + tmp2.subtract(count) + "; " + tmp2 + " " + count);
				count = count.add(tmp2.subtract(count));
				tmp = tmp.divide(prime);
			}
		}

		System.out.println(ans);




	}


	public static void main(String[] args) throws Exception {
		C c = new C();
		c.realMain();
	}
}