#include <bits/stdc++.h>
using namespace std;
namespace shyutsuryoku {
const int STRSZ = 3e5 + 13;
char inbufer[STRSZ];
inline void cscan(string& i) {
  int c = getc(stdin), cnt = 0;
  while (c <= 32) c = getc(stdin);
  while (c > 32) *(inbufer + cnt) = c, c = getc(stdin), ++cnt;
  *(cnt + inbufer) = 0;
  i = inbufer;
}
inline void cprint(string& i) {
  char* second = new char[i.size() + 1];
  strcpy(second, i.c_str());
  while (*second) putchar(*second), second++;
}
inline void cprint(const char*& i) {
  int cnt = 0;
  while (*(i + cnt)) putc(*(i + cnt), stdout), cnt++;
}
inline void cscan(int& i) {
  i = 0;
  int c = getc(stdin), b = 0;
  while (c <= 32) c = getc(stdin);
  if (c == '-') b = 1, c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
  if (b) i = -i;
}
inline void cprint(int i) {
  if (i < 0) putc('-', stdout), i = -i;
  int sz = 0;
  char ans[12];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(long long& i) {
  i = 0;
  int c = getc(stdin), b = 1;
  while (c <= 32) c = getc(stdin);
  if (c == '-') b = -1, c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
  i *= b;
}
inline void cprint(long long i) {
  if (i < 0) putc('-', stdout), i = -i;
  int sz = 0;
  char ans[21];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(unsigned& i) {
  i = 0;
  int c = getc(stdin);
  while (c <= 32) c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
}
inline void cprint(unsigned i) {
  int sz = 0;
  char ans[12];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(unsigned long long& i) {
  i = 0;
  int c = getc(stdin);
  while (c <= 32) c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
}
inline void cprint(unsigned long long i) {
  int sz = 0;
  char ans[21];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(double& i) { scanf("%lf", &i); }
inline void cprint(double i) { printf("%lf", i); }
inline void cprint(char i) { putc(i, stdout); }
inline void cscan(char& i) {
  int b = getc(stdin);
  while (b <= 32) b = getc(stdin);
  i = b;
}
template <class T>
inline void cscan(pair<T, T>& i) {
  cscan(i.first);
  cscan(i.second);
}
template <class T>
inline void cprint(pair<T, T>& i) {
  cprint('(');
  cprint(i.first);
  cprint(' ');
  cprint(i.second);
  cprint(')');
}
template <class T>
inline void cscan(vector<T>& i) {
  for (auto& j : i) cscan(j);
}
template <class T>
inline void cprint(vector<T>& i) {
  for (auto& j : i) cprint(j), cprint(' ');
}
template <class T>
inline void cprint(vector<vector<T> >& i) {
  for (auto& j : i) cprint(j), cprint('\n');
}
template <class T>
ostream& operator,(ostream& os, T v) {
  cprint(v);
  return os;
}
template <class T>
istream& operator,(istream& is, T& v) {
  cscan(v);
  return is;
}
}  // namespace shyutsuryoku
using namespace shyutsuryoku;
void AnimeConservativeRevolution();
int main() {
  srand(time(0));
  AnimeConservativeRevolution();
  return 0;
}
void AnimeConservativeRevolution() {
  int n, k;
  cin, n, k;
  int rz = (n - k) / 2 + 1;
  for (int i = 0; i < n; i++) {
    if (i % rz == rz - 1)
      cout, '1';
    else
      cout, '0';
  }
}

### Prompt

Generate 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;
namespace shyutsuryoku {
const int STRSZ = 3e5 + 13;
char inbufer[STRSZ];
inline void cscan(string& i) {
  int c = getc(stdin), cnt = 0;
  while (c <= 32) c = getc(stdin);
  while (c > 32) *(inbufer + cnt) = c, c = getc(stdin), ++cnt;
  *(cnt + inbufer) = 0;
  i = inbufer;
}
inline void cprint(string& i) {
  char* second = new char[i.size() + 1];
  strcpy(second, i.c_str());
  while (*second) putchar(*second), second++;
}
inline void cprint(const char*& i) {
  int cnt = 0;
  while (*(i + cnt)) putc(*(i + cnt), stdout), cnt++;
}
inline void cscan(int& i) {
  i = 0;
  int c = getc(stdin), b = 0;
  while (c <= 32) c = getc(stdin);
  if (c == '-') b = 1, c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
  if (b) i = -i;
}
inline void cprint(int i) {
  if (i < 0) putc('-', stdout), i = -i;
  int sz = 0;
  char ans[12];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(long long& i) {
  i = 0;
  int c = getc(stdin), b = 1;
  while (c <= 32) c = getc(stdin);
  if (c == '-') b = -1, c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
  i *= b;
}
inline void cprint(long long i) {
  if (i < 0) putc('-', stdout), i = -i;
  int sz = 0;
  char ans[21];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(unsigned& i) {
  i = 0;
  int c = getc(stdin);
  while (c <= 32) c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
}
inline void cprint(unsigned i) {
  int sz = 0;
  char ans[12];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(unsigned long long& i) {
  i = 0;
  int c = getc(stdin);
  while (c <= 32) c = getc(stdin);
  while (c >= '0' && c <= '9') i *= 10, i += c - '0', c = getc(stdin);
}
inline void cprint(unsigned long long i) {
  int sz = 0;
  char ans[21];
  while (i || !sz) ans[sz++] = i % 10 + '0', i /= 10;
  while (sz--) putc(ans[sz], stdout);
}
inline void cscan(double& i) { scanf("%lf", &i); }
inline void cprint(double i) { printf("%lf", i); }
inline void cprint(char i) { putc(i, stdout); }
inline void cscan(char& i) {
  int b = getc(stdin);
  while (b <= 32) b = getc(stdin);
  i = b;
}
template <class T>
inline void cscan(pair<T, T>& i) {
  cscan(i.first);
  cscan(i.second);
}
template <class T>
inline void cprint(pair<T, T>& i) {
  cprint('(');
  cprint(i.first);
  cprint(' ');
  cprint(i.second);
  cprint(')');
}
template <class T>
inline void cscan(vector<T>& i) {
  for (auto& j : i) cscan(j);
}
template <class T>
inline void cprint(vector<T>& i) {
  for (auto& j : i) cprint(j), cprint(' ');
}
template <class T>
inline void cprint(vector<vector<T> >& i) {
  for (auto& j : i) cprint(j), cprint('\n');
}
template <class T>
ostream& operator,(ostream& os, T v) {
  cprint(v);
  return os;
}
template <class T>
istream& operator,(istream& is, T& v) {
  cscan(v);
  return is;
}
}  // namespace shyutsuryoku
using namespace shyutsuryoku;
void AnimeConservativeRevolution();
int main() {
  srand(time(0));
  AnimeConservativeRevolution();
  return 0;
}
void AnimeConservativeRevolution() {
  int n, k;
  cin, n, k;
  int rz = (n - k) / 2 + 1;
  for (int i = 0; i < n; i++) {
    if (i % rz == rz - 1)
      cout, '1';
    else
      cout, '0';
  }
}

```