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.BigInteger;
import java.util.*;
 
 
 
 public class Main {
	public static InputReader in;
    public static PrintWriter pw;
 
 
 
	public static void main(String args[]) {
		new Thread(null, new Runnable() {
            public void run() {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
    }
	//static HashSet<Integer> set;
	static ArrayList<Integer> g[];
	static ArrayList<Integer> h[];
	//static boolean visited[];
	static long edje=0;
    static boolean vis[];
	static int col[];
	static boolean[] visited;
	static int Parent[];
	static int Ans=0;
	static int min=Integer.MAX_VALUE;
	static boolean vis1[];
	static int degree[];
	static int f[];
	static  int size[];
	static int n;
	static int edjes=0;
	static int start=-1;
	static int end=-1;
	static boolean bool=false;
	static int Total=0;
	static int nums[];
	//static int a[];
	static int fr[];
	static int min1=Integer.MAX_VALUE;
	static TreeSet<String> set;
	static int a[];
	static int time1[];
	static int time2[];
	static int glob=0;
	static  HashSet<Integer>[] s;
	static int x,y;
	static StringBuilder p;
	static StringBuilder tmp=new StringBuilder();
	static HashMap<String,String> hm=new HashMap<String,String>();
	
	public static void solve(){
	
		 in = new InputReader(System.in);
		 pw = new PrintWriter(System.out);
	     long n=in.nextLong();
	     int k=in.nextInt();
	     TreeSet<Long> s=new TreeSet<Long>(); 
	     for(long i=1;i<=Math.sqrt(n);i++)
	     {
	         if(n%i==0)
	         {
	             s.add(i);
	             s.add(n/i);
	         }
	     }
	     if(s.size()<k)
	     {
	         System.out.print(-1);
	     }
	     else
	     {
	         int c=0;
	         for(long x:s)
	         {
	          c++;
	          if(c==k)
	          {
	              System.out.print(x);
	              break;
	          }
	         }
	     }
	}
public static int check(int mid,int a[],int b[])
{
    int index=0;
    int i=0;
    int c=0;
    while(index<b.length&&i<a.length)
    {
        if((a[i]-x<=b[index])&&(b[index]<=a[i]+y))
        {
        
            p.append((i+1)+" "+(index+1)+"\n");
            c++;
            i++;
        }
        index++;
    }
   //System.out.println(c+" "+mid+"-----");
    return c;
}
	
	/*
	 SubTree Checker DFS (TO CHECK IF X IS IN A SUBTREE OF Y)
	public static void dfs(int curr)
	{
		visited[curr]=true;
		time1[curr]=glob++;
		for(int x:g[curr])
		{
		if(!visited[x])
			dfs(x);
		}
		time2[curr]=glob++;
	}
    
	
	
 
    /*NO OF EDJES IN WHOLE CONNECTED COMPONENTS
  
	public static void dfs1(int curr)
	{
		visited[curr]=true;
		for(int next:g[curr])
		{
			edje++;
			if(!visited[next])
				dfs1(next);
		}
	}
	/*SUM OF ALL SUBTREE NODE'S VLAUES DFS
	public static void dfs(int curr,int prev)
		{
		val[curr]=1;
			for(int x:g[curr])
			{
				if(x!=prev)
				{
		            dfs(x,curr);
		            val[curr]+=val[x];
					
			    }
			}
		}*/
	
		public static long power(long a,long b)
		{
			long result=1;
			while(b>0)
			{
				if(b%2==1)
					result*=a;
				a=a*a;
				b/=2;
			}
			return result;
		}
				public static long pow(long n,long p,long m)
	{
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	}
	static class Pair implements Comparable<Pair>{
	int y;
		int x;
		Pair(int mr,int i){
	     	y=mr;
			x=i;
			
		}
		@Override
		public int compareTo(Pair o) {
		      //  if(o.dis<this.dis)
		        	return 1;
		       // else
		        //	return -1;
			
			}
		
	}
	public static long gcd(long a, long b) {
		  if (b == 0) return a;
		  return gcd(b, a%b);
		}
	static class InputReader {
 
		private InputStream stream;
		private 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 boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}