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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class PrimeAndMultiplication 
{
	static LinkedList<Integer> primes=new LinkedList<>();
	static int MOD=(int)1e9+7;

	public static void main(String[] args) 
	{
		
		InputStream is=System.in;
		OutputStream out=System.out;
		
		FastScanner input=new FastScanner(is);
		FastPrinter output=new FastPrinter(out);
		int x=input.nextInt();
		long n=input.nextLong();
		prime(x );
        output.println(f(n));
        output.flush();
	}

	
	static long f(long n) 
	  {
		long ans=1;
				for(int off:primes)
				{
				   long pow=0;
				   long primeFactor=off;
				   while(true) 
				    {
					    pow+=(n/primeFactor);
					     if((n/primeFactor)<off) 
					     {
					    	 break; 
					     }
					     primeFactor=primeFactor*off;
				    }
				   ans=  (ans*power(off,pow))%MOD;
				}
		return ans;
	  }
	
	
	public static long power(long p,long k) 
	  {
		long res=1;
		p%=MOD;
		while(k>0) 
		{
			if((k&1)==1) 
			{
				res=(res*p)%MOD;
			}
			p=(p*p)%MOD;
			k>>=1;
		}
		return res;
	  }
	
	
	static void prime(int x) 
	  {
		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(x);
		}
	 }

}

class FastPrinter extends PrintWriter
 {
	 public FastPrinter(OutputStream out) 
	 {
		super(out);
	 }
	 public FastPrinter(Writer out) 
	 {
		super(out);
	 }
}

class FastScanner
{
	BufferedReader br;
	StringTokenizer st;
   public FastScanner(InputStream is) 
    {
	  br=new BufferedReader(new InputStreamReader(is)); 
    }
   
   public FastScanner(File f) 
   {
	   try 
	    {
		 br=new BufferedReader(new FileReader(f));
     	} 
	   catch (FileNotFoundException e) 
	    {
    		e.printStackTrace();
	    }
   }
   
   public String next()
    {
	  while(st==null||!st.hasMoreElements()) 
	   {
		  String s=null;
		  try 
		  {
		    s=br.readLine();
		   }
		  catch(IOException e) 
		  {
			  e.printStackTrace();
		  }
		  if(s==null) 
		  {
			  return null;
		  }
		  st=new StringTokenizer(s);
	   } 
	  return st.nextToken();
    }
   
   public int nextInt() 
   {
	return Integer.parseInt(next());   
   }
   public long nextLong() 
   {
	   return Long.parseLong(next());
   }
}
