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.
//package cf589d2;
import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class C {
	static long MOD = 1000000007L;
	static boolean prime(long x) {
		if(x == 1) return false;
		for(long i = 2; i * i <= x; i++)
			if(x % i == 0)
				return false;
		return true;
	}
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		long x = sc.nextLong(), n = sc.nextLong();
		TreeSet<Long> p = new TreeSet<Long>();
		for(long i = 1; i * i <= x; i++)
			if(x % i == 0) {
				if(prime(i))
					p.add(i);
				if(prime(x / i))
					p.add(x / i);
			}
		long ans = 1;
		for(long l : p) {
			long xx = 1;
			while((xx * l) > 0 && n / xx >= l) {
				xx *= l;
				ans = ans * pMod(l, n / xx) % MOD;
			}
		}
		out.println(ans);
		out.close();
	}
	public static long pMod(long x, long p) {
		if(p == 0)
			return 1;
		long l = pMod(x, p / 2);
		return l * l % MOD * (p % 2 == 1 ? x : 1) % MOD;
	}
	public static PrintWriter out  = new PrintWriter(new BufferedOutputStream(System.out));
	public static class MyScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		String next() {
			while (st == null || !st.hasMoreElements())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}
