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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class A {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static PrintWriter out = new PrintWriter(System.out);

	static void solve() throws Exception {
		long n = nextLong(), k = nextLong();
		long cant = 0;
		long ret = -1;
		boolean isSquared = false;
		for (long div = 1; div * div <= n; div++) {
			if (div * div == n) {
				isSquared = true;
			}
			if (n % div == 0) {
				cant++;
			}
			if (cant == k) {
				ret = div;
				break;
			}
		}
		if (ret == -1) {
			long saco = k - cant;
			if (isSquared) {
				cant--;
			}
			long newK = cant - saco + 1;
			long newc = 0;
			for (long div = 1; div * div <= n; div++) {
				if (n % div == 0) {
					newc++;
				}
				if (newc == newK) {
					ret = n / div;
					break;
				}
			}
		}
		out.println(ret);
	}

	public static void main(String[] args) throws Exception {
		solve();
		out.close();
	}

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

	static int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(next());
	}

	static long nextLong() throws Exception {
		return Long.parseLong(next());
	}

}