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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Objects;
import java.util.Random;
import java.util.StringTokenizer;

public class Solution{
	
	static long mod = (long)1e9+7;
	
	
	
	public static void main(String[] args) {

		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
		int tt = 1;
		while(tt-->0) {
			
			long x = fs.nextLong();
			long n = fs.nextLong();
			
			
			ArrayList<Integer> primes = new ArrayList<Integer>();
			for(int i=2;i*i<=x;i++) {
				if(x%i==0) {
					primes.add(i);
					while(x%i==0) {
						x /= i;
					}
				}
			}
			if(x>1) primes.add((int)x);
			
			
			long ans = 1L;
			
			for(int p: primes) {
				long exp = 1L;
				while(exp <= n/p) {
					exp *= p;
				}
				if(exp==1) continue;
				ans = mul(ans, bExp(exp%mod,n/exp));
				exp /= p;
				while(exp>1) {
					ans = mul(ans, bExp(exp%mod, n/exp - n/(exp*p)));
					exp /= p;
				}
			}
			
			out.println(ans);
			
		}
		
		out.close();
		
	}
	
	static long mul(long a, long b) {
		return ((a%mod)*(b%mod))%mod;
	}
	
	
	static long bExp(long a, long n) {
		long res = 1;
		while(n>0) {
			if((n&1)==1) {
				res = mul(res, a);
			}
			a = mul(a,a);
			n = n>>1;
		}
		return res;
	}
	
	
	
	
	static final Random random=new Random();
	
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	
	static class FastScanner{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		public String next(){
			while(!st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				} catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		public String nextLine() throws IOException {
			return br.readLine();
		}
		
		public int nextInt(){
			return Integer.parseInt(next());
		}

		public int[] readArray(int n){
			int[] a = new int[n];
			for(int i=0;i<n;i++)
				a[i] = nextInt();
			return a;
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public char nextChar() {
			return next().toCharArray()[0];
		}
	}
	
}
