#include <bits/stdc++.h>
using namespace std;
string str;
int k;
void ff() {
  int mn = -1;
  for (int i = 1; i <= str.size(); i++) {
    for (int j = 0; j + i <= str.size(); j++) {
      string s;
      int a = 0;
      for (int k = 0; k < i; k++) s += str[j + k];
      for (int k = 0; k < str.size() - s.size() + 1; k++) {
        int y = 1;
        for (int p = 0; p < s.size(); p++) {
          if (s[p] != str[p + k]) {
            y = 0;
          }
        }
        a += y;
      }
      if (a == 1) {
        if (mn == -1) {
          mn = s.size();
        }
      }
      if (a == 1 && mn == k && s.size() == mn) {
        cout << str << endl;
        cout << s << endl << endl;
      }
    }
  }
}
void f(int n) {
  if (n == 0) {
    ff();
    return;
  }
  str[n - 1] = '1';
  f(n - 1);
  str[n - 1] = '0';
  f(n - 1);
}
int main() {
  int n;
  cin >> n >> k;
  string s;
  for (int i = 0; i < n; i++) {
    s += '0';
    str += '0';
  }
  if (k == 1) {
    s[0] = '1';
    cout << s << endl;
    return 0;
  }
  if (k == 2) {
    s[0] = '1';
    s[1] = '1';
    cout << s << endl;
    return 0;
  }
  if (k < (n + 2) / 3) {
    s[k - 2] = '1';
    s[k * 2 - 3] = '1';
    cout << s << endl;
    return 0;
  } else {
    int t = (n - k) / 2;
    for (int i = 0; i < t; i++) {
      for (int j = i; j < n; j += t + 1) {
        s[j] = '1';
      }
    }
  }
  cout << s << endl;
}

### Prompt

Please create a solution in cpp to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
string str;
int k;
void ff() {
  int mn = -1;
  for (int i = 1; i <= str.size(); i++) {
    for (int j = 0; j + i <= str.size(); j++) {
      string s;
      int a = 0;
      for (int k = 0; k < i; k++) s += str[j + k];
      for (int k = 0; k < str.size() - s.size() + 1; k++) {
        int y = 1;
        for (int p = 0; p < s.size(); p++) {
          if (s[p] != str[p + k]) {
            y = 0;
          }
        }
        a += y;
      }
      if (a == 1) {
        if (mn == -1) {
          mn = s.size();
        }
      }
      if (a == 1 && mn == k && s.size() == mn) {
        cout << str << endl;
        cout << s << endl << endl;
      }
    }
  }
}
void f(int n) {
  if (n == 0) {
    ff();
    return;
  }
  str[n - 1] = '1';
  f(n - 1);
  str[n - 1] = '0';
  f(n - 1);
}
int main() {
  int n;
  cin >> n >> k;
  string s;
  for (int i = 0; i < n; i++) {
    s += '0';
    str += '0';
  }
  if (k == 1) {
    s[0] = '1';
    cout << s << endl;
    return 0;
  }
  if (k == 2) {
    s[0] = '1';
    s[1] = '1';
    cout << s << endl;
    return 0;
  }
  if (k < (n + 2) / 3) {
    s[k - 2] = '1';
    s[k * 2 - 3] = '1';
    cout << s << endl;
    return 0;
  } else {
    int t = (n - k) / 2;
    for (int i = 0; i < t; i++) {
      for (int j = i; j < n; j += t + 1) {
        s[j] = '1';
      }
    }
  }
  cout << s << endl;
}

```