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.*;
import java.util.*;

import javax.swing.event.TreeExpansionEvent;

public class tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int n, z, k;
	static long mod = (long) 1e9 + 7;
	static int[][][] memo;
	static String s, t;
	static ArrayList<int[]>[] ad, ad2;
	static TreeMap<Long, Integer>[] gs;
	static long inf = Long.MAX_VALUE;
	static ArrayList<Integer> o;
	static char[][] g;
	static boolean[] vis;
	static long[] f;
	static int nodes;
	static int[][] nxt;
	static int[] a, arr, pre;
	static int sum, ans, max;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		long x = sc.nextLong();
		long n = sc.nextLong();
		long ans = 1;
		ArrayList<Integer> a = new ArrayList<>();
		for (int i = 2; i <= x / i; i++)
			if (x % i == 0) {
				a.add(i);
				while (x % i == 0)
					x /= i;
			}
		if (x != 1)
			a.add((int) x);
		for (int i = 0; i < a.size(); i++) {
			long num = a.get(i);
			while (true) {
				if (num * a.get(i) <= 0 || num > n / a.get(i))
					break;
				num = num * 1l * a.get(i);
			}
			long pre = 0;
			while (num > 1) {
				long cnt = (((n / num)) - pre);
				long num1 = num % mod;
				long tem = modPow(num1, cnt);
			//	System.out.println(num + " " + num1 + " " + cnt + " " + tem);
				ans = (ans * tem) % mod;
				pre = n / num;
				num /= a.get(i);
			}
		}
		System.out.println(ans);
		out.flush();
	}

	static long modPow(long a, long e)

	{
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1;
		}
		return res;
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}