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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.math.BigInteger;

public class C {
	
	private static long mod = 1000000007;

	public static void main(String[] args) throws Exception {
//		BufferedReader br = new BufferedReader(new FileReader("F:/books/input.txt"));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] s = br.readLine().split(" ");
		Long x = Long.parseLong(s[0]);
		Long n = Long.parseLong(s[1]);
		long prod = 1;
		
		for (int i = 2; i <= Math.sqrt(x); i++) {
			if(x%i==0) {
				while(x%i==0) x/=i;
				prod = mulMod(prod,calc(i,n),mod);//(prod * calc(i,n))%mod;
			}
		}
		if(x>1) prod = mulMod(prod,calc(x,n),mod);//(prod * calc(x,n))%mod;
		System.out.println(prod);
	}

	private static long calc(long x, Long n) {
		BigInteger tot = BigInteger.ZERO;
		BigInteger box = BigInteger.valueOf(x);
		BigInteger bx = BigInteger.valueOf(x);
		BigInteger bn = BigInteger.valueOf(n);
		while(bn.compareTo(bx)>=0) {
			tot = tot.add(bn.divide(bx));
			bx = bx.multiply(box);
		}
		return box.modPow(tot, BigInteger.valueOf(mod)).longValue();
	}
	
	private static long mulMod(long x,long y,long mod) {
		BigInteger bx = BigInteger.valueOf(x);
		BigInteger by = BigInteger.valueOf(y);
		BigInteger bmod = BigInteger.valueOf(mod);
		return bx.multiply(by).mod(bmod).longValue();
	}
	
}
