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.io.*;
import java.util.*;

public class Main implements Runnable{
    public static void main(String[] args) throws Exception {
        //new Thread(null,new Main(),"Thread-1",1024*1024*10).start();
        new Main().solve();
    }
    void solve() throws Exception{
        InputReader in=new InputReader(System.in);
        PrintWriter out=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n=in.nextInt(),k=in.nextInt();
        if(k==1) {
            for(int i=0;i<n-1;i++) out.print(1);
            out.print(0);
        }else {
            int loop = (n - k) / 2 + 1;
            int[] s = new int[k];
            int[] s1 = new int[(n + 1) / 2 + k / 2 - 1];
            for (int i = 0; i < k; i += loop) {
                s[i] = 1;
            }
            for (int i = 0; i < k - 1; i++) {
                s1[i] = s[i + 1];
                s1[i + loop - 1] = s[i];
            }
            for (int i = 0; i < s1.length; i++) out.print(s1[i]);
            for (int i = s1.length - loop; i < s1.length; i++) out.print(s1[i]);
        }
        out.flush();
    }
    @Override
    public void run() {
        try {
            solve();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    void shuffle(int[]a,int l,int r){
        Random rnd=new Random();
        for (int i=r; i>l+1; i--) {
            int j=rnd.nextInt(i),tmp=a[j];
            a[j]=a[i-1];
            a[i-1]=tmp;
        }
    }
    void shuffle(Object[]a,int l,int r){
        Random rnd=new Random();
        for (int i=r; i>l+1; i--) {
            int j=rnd.nextInt(i);
            Object tmp=a[j];
            a[j]=a[i-1];
            a[i-1]=tmp;
        }
    }
    void shuffle(long[]a,int l,int r){
        Random rnd=new Random();
        for (int i=r; i>l+1; i--) {
            int j=rnd.nextInt(i);
            long tmp=a[j];
            a[j]=a[i-1];
            a[i-1]=tmp;
        }
    }
    class InputReader{
        StreamTokenizer tokenizer;
        public InputReader(InputStream stream){
            tokenizer=new StreamTokenizer(new BufferedReader(new InputStreamReader(stream)));
            tokenizer.ordinaryChars(33,126);
            tokenizer.wordChars(33,126);
        }
        public String next() throws IOException {
            tokenizer.nextToken();
            return tokenizer.sval;
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public boolean hasNext() throws IOException {
            int res=tokenizer.nextToken();
            tokenizer.pushBack();
            return res!=tokenizer.TT_EOF;
        }
    }
}