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.math.BigInteger;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	static final int MODULUS = 1_000_000_007;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int x = sc.nextInt();
		long n = sc.nextLong();
		System.out.println(solve(x, n));

		sc.close();
	}

	static int solve(int x, long n) {
		List<Integer> primeFactors = buildPrimeFactors(x);

		int result = 1;
		for (int primeFactor : primeFactors) {
			result = multiplyMod(result, powMod(primeFactor, computeFactorNum(primeFactor, n)));
		}

		return result;
	}

	static int multiplyMod(int x, int y) {
		return (int) ((long) x * y % MODULUS);
	}

	static int powMod(int base, long exponent) {
		return BigInteger.valueOf(base).modPow(BigInteger.valueOf(exponent), BigInteger.valueOf(MODULUS)).intValue();
	}

	static long computeFactorNum(int primeFactor, long n) {
		return (n == 0) ? 0 : (n / primeFactor + computeFactorNum(primeFactor, n / primeFactor));
	}

	static List<Integer> buildPrimeFactors(int x) {
		List<Integer> primeFactors = new ArrayList<>();
		for (int i = 2; i * i <= x; ++i) {
			if (x % i == 0) {
				primeFactors.add(i);

				while (x % i == 0) {
					x /= i;
				}
			}
		}
		if (x != 1) {
			primeFactors.add(x);
		}

		return primeFactors;
	}
}
