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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.InputMismatchException;

public class A {

	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		InputReader s = new InputReader(System.in);
		PrintWriter p = new PrintWriter(System.out);
		long n = s.nextLong();
		int k = s.nextInt();
		if (k > 2 * Math.sqrt(n)) {
			p.println(-1);
			p.flush();
			return;
		}
		int flag = 0;
		ArrayList<Long> factors1 = new ArrayList<>();
		ArrayList<Long> factors2 = new ArrayList<>();
		for (long i = 1; i <= Math.sqrt(n); i++) {
			if (n % i == 0) {
				long val1 = i;
				factors1.add(i);
				long val2 = n / i;
				if (val2 > Math.sqrt(n))
					factors2.add(val2);
			}
		}
		//System.out.println(factors1);
		//System.out.println(factors2);
		Collections.reverse(factors2);
		if (k <= factors1.size()) {
			p.println(factors1.get(k - 1));
		} else {
			k -= factors1.size();
			if (k > factors2.size()) {
				p.println(-1);
			} else {
				p.println(factors2.get(k - 1));
			}
		}

		p.flush();
		p.close();
	}

	public static void dfs(ArrayList[] adj, int ci, int[] vis) {
		if (vis[ci] == 1) {
			return;
		}
		vis[ci] = 1;
		ArrayList<Integer> nbrs = adj[ci];
		for (int i = 0; i < nbrs.size(); i++) {
			if (vis[nbrs.get(i)] == 0) {
				dfs(adj, nbrs.get(i), vis);
			}
		}
	}

	public static class node {
		int index;
		HashMap<Integer, Integer> nbrs;

		node(int i) {
			this.index = i;
			this.nbrs = new HashMap<>();
		}
	}

	public static void union(int[] arr, int[] size, int a, int b) {
		int root_a = root(arr, a);
		int root_b = root(arr, b);
		if (size[root_a] >= size[root_b]) {
			arr[root_b] = root_a;
			size[root_a] += size[root_b];
		} else {
			arr[root_a] = root_b;
			size[root_b] += size[root_a];
		}
	}

	public static int root(int[] arr, int i) {
		while (arr[i] != i) {
			i = arr[i];
		}
		return i;
	}

	static class pair implements Comparable<pair> {
		Integer x, y;

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

		public int compareTo(pair o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);

			return result;
		}

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

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x - x == 0 && p.y - y == 0;
			}
			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}
	}

	public static ArrayList Divisors(long n) {
		ArrayList<Long> div = new ArrayList<>();

		for (long i = 1; i <= Math.sqrt(n); i++) {
			if (n % i == 0) {
				div.add(i);

				if (n / i != i)
					div.add(n / i);
			}
		}
		return div;
	}

	public static int BinarySearch(long[] a, long k) {
		int n = a.length;
		int i = 0, j = n - 1;
		int mid = 0;

		if (k < a[0])
			return 0;
		else if (k >= a[n - 1])
			return n;
		else {
			while (j - i > 1) {
				mid = (i + j) / 2;

				if (k >= a[mid])
					i = mid;
				else
					j = mid;
			}
		}

		return i + 1;
	}

	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static long LCM(long a, long b) {
		return (a * b) / GCD(a, b);
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

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

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

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

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

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

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

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

	static class CodeX {
		public static void sort(long arr[]) {
			merge_sort(arr, 0, arr.length - 1);
		}

		private static void merge_sort(long A[], long start, long end) {
			if (start < end) {
				long mid = (start + end) / 2;
				merge_sort(A, start, mid);
				merge_sort(A, mid + 1, end);
				merge(A, start, mid, end);
			}

		}

		private static void merge(long A[], long start, long mid, long end) {
			long p = start, q = mid + 1;
			long Arr[] = new long[(int) (end - start + 1)];
			long k = 0;

			for (int i = (int) start; i <= end; i++) {
				if (p > mid)
					Arr[(int) k++] = A[(int) q++];

				else if (q > end)
					Arr[(int) k++] = A[(int) p++];

				else if (A[(int) p] < A[(int) q])
					Arr[(int) k++] = A[(int) p++];

				else
					Arr[(int) k++] = A[(int) q++];
			}
			for (int i = 0; i < k; i++) {
				A[(int) start++] = Arr[i];
			}

		}

	}

}