#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void checkmin(T &a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T &a, T b) {
  if (b > a) a = b;
}
int N, K;
char cs[100002];
int main() {
  scanf("%d%d", &N, &K);
  for (int i = (0); i < (int)(N); i++) cs[i] = '1';
  for (int i = (0); i < (int)(K); i++) cs[i] = '0';
  cs[N] = 0;
  if (K > 1 && K != N) {
    int cnt = (N - K) / 2;
    for (int i = 0; i < N; i += cnt + 1) {
      for (int j = 0; j < cnt + 1 && i + j < N; j++) {
        if (j == 0)
          cs[i + j] = '0';
        else
          cs[i + j] = '1';
      }
    }
  }
  printf("%s\n", cs);
}

### Prompt

Your challenge is to write a Cpp solution 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;
template <class T>
inline void checkmin(T &a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T &a, T b) {
  if (b > a) a = b;
}
int N, K;
char cs[100002];
int main() {
  scanf("%d%d", &N, &K);
  for (int i = (0); i < (int)(N); i++) cs[i] = '1';
  for (int i = (0); i < (int)(K); i++) cs[i] = '0';
  cs[N] = 0;
  if (K > 1 && K != N) {
    int cnt = (N - K) / 2;
    for (int i = 0; i < N; i += cnt + 1) {
      for (int j = 0; j < cnt + 1 && i + j < N; j++) {
        if (j == 0)
          cs[i + j] = '0';
        else
          cs[i + j] = '1';
      }
    }
  }
  printf("%s\n", cs);
}

```