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.FileReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class C {
	static InputReader in = new InputReader("");

	public static void main(String[] args) {
		StringBuilder sb = new StringBuilder();

		long x = in.nextLong(), n = in.nextLong();
		ArrayList<Long> primes = new ArrayList<>();
		for (long i = 2; i*i <= x; i++) {
			if (x % i != 0)
				continue;
			primes.add(i);
			while (x % i == 0)
				x /= i;
		}
		if (x > 1)
			primes.add(x);
		long ans = 1, MOD = 1_000_000_007;
		for (long p : primes) {
			long val;
			for (val = 1; val <= n / p; val *= p);
			long cur = 0, prev = 0;
			while (val > 1) {
				cur = (n / val) - prev;
				cur = pow(val % MOD, cur, MOD);
				ans = (ans * cur) % MOD;
				prev = n / val;
				val /= p;
			}
		}
		sb.append(ans);
		
		System.out.println(sb.toString().trim());
	}

	static long pow(long a, long b, long MOD) {
		if (b <= 0)
			return 1;
		long res = pow(a, b / 2, MOD);
		res = (res * res) % MOD;
		if (b % 2 != 0)
			res = (res * a) % MOD;
		return res;
	}
	
	
	static class InputReader {
		private BufferedReader reader;
		private StringTokenizer tokenizer;

		public InputReader(String filename) {
			try {
				if (filename.length() == 0)
					reader = new BufferedReader(new InputStreamReader(System.in));
				else
					reader = new BufferedReader(new FileReader(filename));
			} catch (Exception e) {
			}
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (Exception e) {
				return tokenizer.nextToken();
			}
		}

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

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}

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

		public int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
			return array;
		}

		public double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
			return array;
		}

		public long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
			return array;
		}

	}

}
