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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;
import java.io.BufferedReader;

public class C {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskF solver = new TaskF();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskF {
		private Set<Integer> prime(int n) {
			Set<Integer> s = new HashSet<>();
			if (n % 2 == 0) {
				s.add(2);
				while (n > 0 && n % 2 == 0) {
					n = n / 2;
				}
			}
			if (n % 3 == 0) {
				s.add(3);
				while (n > 0 && n % 3 == 0) {
					n = n / 3;
				}
			}
			for (int i = 5; i * i <= n; i += 2) {
				if (n % i == 0) {
					s.add(i);
					while (n > 0 && n % i == 0) {
						n = n / i;
					}
				}
			}
			if (n > 1) {
				s.add(n);
			}
			return s;
		}

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int x = in.nextInt();
			long n = in.nextLong();
			Set<Integer> fac = prime(x);
			long ans = 1;
			long mod = 1000000007;
			for (Integer f : fac) {
				long t = n;
				long div = t / f;
				while (div > 0) {
					ans = (ans * (power(f, div)) % mod) % mod;
					t /= f;
					div = t / f;
				}
			}
			out.println(ans);
		}

		private long power(long x, long y) {
			long res = 1;
			long mod = 1000000007;
			while (y > 0) {
				if (y % 2 == 1)
					res = (res * x) % mod;
				y = y >> 1;
				x = (x * x) % mod;
			}
			return res;
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}