Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. 

For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l.

Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him.

You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k.

Input

The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)).

Output

Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string.

Examples

Input


4 4


Output


1111

Input


5 3


Output


01010

Input


7 3


Output


1011011

Note

In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4.

In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3.

In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
import java.util.*;
//import java.math.BigLongeger; 
public class Boss {
	//static long c=0;
	//static HashMap<Integer,Long> hm2=new HashMap<Integer,Long>();
	public static void main(String[] args)
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		if(k==1)
		{
			StringBuilder ans=new StringBuilder("1");
			for(int i=1;i<n;i++)
				ans.append("0");
			//ans.append("0");
			System.out.print(ans);
			return;
		}
		int z=(n-k)/2;
		StringBuilder ans=new StringBuilder("1");
		for(int i=0;i<z;i++)
			ans.append("0");
		int l=ans.length();
		int num=n/l;
		String t=ans.toString();
		for(int i=1;i<num;i++)
			ans.append(t);
		for(int i=0;i<n%l;i++)
		{
			ans.append(t.charAt(i));
		}
		System.out.print(ans);
	} 
}

