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.lang.*;
import java.io.*;

public class Temp {
	static int imax = Integer.MAX_VALUE, imin = Integer.MIN_VALUE;
	static long lmax = Long.MAX_VALUE, lmin = Long.MIN_VALUE;
	static long mod = (long) 1e9 + 7;

	public static void main(String[] args) throws java.lang.Exception {
		// File file=new File("C:\\Users\\EagleEye\\Desktop\\input.txt");
		// File file1=new File("C:\\Users\\EagleEye\\Desktop\\output.txt");
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		// int test=in.ni();
		int test = 1;
		int i = 0, j = 0;
		while (test-- > 0) {
			long n = in.nl();
			int k = in.ni();
			int cnt = 1;
			ArrayList<Long> list = new ArrayList<>();
			for (i = 1; i <= Math.sqrt(n); i++) {
				if (n % i == 0) {
					list.add((long) i);
					if (i != n / i) {
						list.add(n / i);
					}
				}
			}
			Collections.sort(list);
			// System.out.println(list);
			if (list.size() < k)
				out.println("-1");
			else
				out.println(list.get(k - 1));
		}
		out.close();
	}

	static class Pair {
		int x, y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public String toString() {
			return x + " " + y;
		}
	}

	static void print(int arr[], int len) {
		for (int i = 0; i < len; i++)
			System.out.print(arr[i] + " ");
		System.out.println();
	}

	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int ni() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c & 15;
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nl() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c & 15;
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String ns() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public char[] ncs() {
			return ns().toCharArray();
		}

		public String nLine() {
			int c = read();
			// while (c != '\n' && c != '\r' && c != '\t' && c != -1)
			// c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (c != '\n' && c != '\r' && c != '\t' && c != -1);
			return res.toString();
		}

		public static boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

	}

}