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.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class Primes_and_Multiplication {

	public static void main(String[] args) {
		Scanner t = new Scanner(System.in);
		int x = t.nextInt();
		long n = t.nextLong();
		ArrayList<Integer> pf = prime_fact(x);

		long ans = 1, temp1 = n;
		for (int i = 0; i < pf.size(); i++) {
			int temp = pf.get(i);
			long pow = 0;

			while (n > 0) {
				pow += n / temp;
				n = n / temp;
			}

			ans = ans * evaluate(temp, pow);
			if (ans >= 1000000007) {
				ans = ans % 1000000007;
			}
			n = temp1;
		}
		System.out.println(ans);
	}

	public static ArrayList<Integer> prime_fact(int n) {
		ArrayList<Integer> pf = new ArrayList<>();
		HashSet<Integer> pfs = new HashSet<>();
		;

		while (n % 2 == 0) {
			if (!pfs.contains(2)) {
				pfs.add(2);
				pf.add(2);
			}
			n = n / 2;
		}

		for (int i = 3; i <= Math.sqrt(n); i++) {
			while (n % i == 0) {
				if (!pfs.contains(i)) {
					pfs.add(i);
					pf.add(i);
				}
				n = n / i;
			}
		}

		if (n > 2) {
			if (!pfs.contains(n)) {
				pfs.add(n);
				pf.add(n);
			}
		}
		return pf;
	}

	public static long evaluate(int temp, long pow) {
		if (pow == 0) {
			return 1;
		}

		else {
			long ans = evaluate(temp, pow / 2);

			if (ans >= 1000000007) {
				ans = ans % 1000000007;
			}

			ans = ans * ans;

			if (ans >= 1000000007) {
				ans = ans % 1000000007;
			}

			if (pow % 2 == 1) {
				ans = ans * temp;
			}

			if (ans >= 1000000007) {
				ans = ans % 1000000007;
			}

			return ans;

		}
	}

}