Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class p762A {
	static List<Integer> list;
	public static void main(String[] args) throws IOException {
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		StringTokenizer st = new StringTokenizer(f.readLine());
		long n = Long.parseLong(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		out.println(solve(n, k));
		out.close();
	}
	
	public static long solve(long n, long k)
	{
		load((int)Math.sqrt(n) + 1);
		int s = 1;
		int e = countDivisors(n);
		if(e < k)
			return -1;
		for(long i = 1; i * i <= n; i++)
		{
			if(n % i == 0)
			{
				if(s == k)
					return i;
				else if(e == k)
					return n / i;
				s++;
				e--;
			}
		}
		return -1;
	}
	
	public static int countDivisors(long n)
	{
		int count = 1;
		for(int p : list)
		{
			if(p * p > n)
				break;
			int e = 0;
			while(n % p == 0)
			{
				n /= p;
				e++;
			}
			count *= e + 1;
		}
		if(n != 1)
			count <<= 1;
		return count;
	}
	
	public static void load(int size)
	{
		list = new ArrayList<Integer>();
		boolean[] a = new boolean[size + 1];
		for(int i = 2; i * i <= size; i++)
			if(!a[i])
				for(int j = i * i; j <= size; j += i)
					a[j] = true;
		for(int i = 2; i <= size; i++)
			if(!a[i])
				list.add(i);
	}
}