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.*;
import java.math.*;
import java.util.*;

public class A {
	final static int MOD = 1000000007;
	static ArrayList<Long> divisors = new ArrayList<>();

	public static void main(String[] args) throws Exception {
		FastReader in = new FastReader(System.in);
		long n = in.nextLong();
		int k = in.nextInt();
		long sqrtN = (long) Math.sqrt(n);
		int i = 1;
		int count = 0;
		while (i <= sqrtN) {
			if (n % i == 0) {
				divisors.add((long) i);
				count++;
			}
			i++;
		}
		if ((double)sqrtN == (double)n / (double)sqrtN)
			count--;
		for (int j = count - 1; j >= 0; j--) {
			divisors.add((long) (n / divisors.get(j)));
		}
		if (k > divisors.size()) {
			System.out.println(-1);
			return;
		}
		System.out.println(divisors.get(k - 1));
	}
	
	static class Pair implements Comparable<Pair> {
		long a, b;
 
		public Pair(long a, long b) {
			this.a = a;
			this.b = b;
		}
 
		public int compareTo(Pair o) {
			if (this.a != o.a)
				return Long.compare(this.a, o.a);
			else
				return Long.compare(this.b, o.b);
		}
 
		public boolean equals(Object o) {
			if (o instanceof Pair) {
				Pair p = (Pair) o;
				return p.a == a && p.b == b;
			}
			return false;
		}
 
		public int hashCode() {
			return new Long(a).hashCode() * 31 + new Long(b).hashCode();
		}
		
		public String toString() {
			return "(" + this.a + "," + this.b + ")";
		}
	}

	static class FastReader {
	    private boolean finished = false;

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

	    public FastReader(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 peek() {
	        if (numChars == -1) {
	            return -1;
	        }
	        if (curChar >= numChars) {
	            curChar = 0;
	            try {
	                numChars = stream.read(buf);
	            } catch (IOException e) {
	                return -1;
	            }
	            if (numChars <= 0) {
	                return -1;
	            }
	        }
	        return buf[curChar];
	    }

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

	    public long nextLong() {
	        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 - '0';
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public String nextString() {
	        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 boolean isSpaceChar(int c) {
	        if (filter != null) {
	            return filter.isSpaceChar(c);
	        }
	        return isWhitespace(c);
	    }

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

	    private String readLine0() {
	        StringBuilder buf = new StringBuilder();
	        int c = read();
	        while (c != '\n' && c != -1) {
	            if (c != '\r') {
	                buf.appendCodePoint(c);
	            }
	            c = read();
	        }
	        return buf.toString();
	    }

	    public String nextLine() {
	        String s = readLine0();
	        while (s.trim().length() == 0)
	            s = readLine0();
	        return s;
	    }

	    public String nextLine(boolean ignoreEmptyLines) {
	        if (ignoreEmptyLines) {
	            return nextLine();
	        } else {
	            return readLine0();
	        }
	    }

	    public BigInteger nextBigInteger() {
	        try {
	            return new BigInteger(nextString());
	        } catch (NumberFormatException e) {
	            throw new InputMismatchException();
	        }
	    }

	    public char nextCharacter() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        return (char) c;
	    }

	    public double nextDouble() {
	        int c = read();
	        while (isSpaceChar(c))
	            c = read();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = read();
	        }
	        double res = 0;
	        while (!isSpaceChar(c) && c != '.') {
	            if (c == 'e' || c == 'E') {
	                return res * Math.pow(10, nextInt());
	            }
	            if (c < '0' || c > '9') {
	                throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        }
	        if (c == '.') {
	            c = read();
	            double m = 1;
	            while (!isSpaceChar(c)) {
	                if (c == 'e' || c == 'E') {
	                    return res * Math.pow(10, nextInt());
	                }
	                if (c < '0' || c > '9') {
	                    throw new InputMismatchException();
	                }
	                m /= 10;
	                res += (c - '0') * m;
	                c = read();
	            }
	        }
	        return res * sgn;
	    }

	    public boolean isExhausted() {
	        int value;
	        while (isSpaceChar(value = peek()) && value != -1)
	            read();
	        return value == -1;
	    }

	    public String next() {
	        return nextString();
	    }

	    public SpaceCharFilter getFilter() {
	        return filter;
	    }

	    public void setFilter(SpaceCharFilter filter) {
	        this.filter = filter;
	    }

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