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.util.*;
import java.io.*;
import java.math.BigInteger;
 
public class Main
{
	static final int mod = (int)1e9+7;
	static long ans;
	public static void main(String[] args) throws Exception
	{
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		long m = in.nextLong();
		long n = in.nextLong();
		ans = 1;
		for(long i = 2; i * i <= m; i++)
		{
			boolean f = false;
			while(m % i == 0)
			{
				f = true;
				m /= i;
			}
			if(!f)
				continue;
			solve(i, n);
		}
		if(m != 1)
			solve(m, n);
		out.println(ans);
		out.flush();
	}

	static void solve(long f, long n)
	{
		long a = 0, n1 = n;

		while(n1 >= f)
		{
			a++;
			n1 /= f;
		}
		n1 = 1;
		for(int i = 0; i < a; i++)
		{
			n1 *= f;
		}
		long sum = 0;
		while(n1 > 1)
		{
			long n2 = n / n1 - sum;
			ans = (ans * fastMod(n1, n2)) % mod;
			sum += n2;
			n1 /= f;
		}
	}

	static long fastMod(long a, long p)
	{
		a %= mod;
		long r = 1;

		while(p > 0)
		{
			if((p & 1) == 1)
				r = (r * a) % mod;
			p >>= 1;
			a = (a * a) % mod;
		}

		return r;
	}
}
 
class FastReader
{
	BufferedReader br;
	StringTokenizer st;
 
	public FastReader()
	{
	    br = new BufferedReader(new InputStreamReader(System.in));
	}
 
	public String next() throws IOException
	{
	    if(st == null || !st.hasMoreElements())
	    {
	        st = new StringTokenizer(br.readLine());
	    }
	    return st.nextToken();
	}
 
	public int nextInt() throws IOException
	{
	    return Integer.parseInt(next());
	}
 
	public long nextLong() throws IOException
	{
	    return Long.parseLong(next());
	}
 
	public String nextLine() throws IOException
	{
		return br.readLine();
	}
}