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.
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse2")
using namespace std;
const long long hell = 1000000007;
long long power(long long a, long long b) {
  if (b == 0) return 1;
  if (b == 1) return a;
  long long t = power(a, b / 2);
  t %= hell;
  t *= t;
  t %= hell;
  if (b % 2)
    return (t * a) % hell;
  else
    return t;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b - a % b, a % b);
}
long long digitsum(long long x) {
  while (x > 9) {
    long long ans = 0;
    while (x != 0) {
      ans += x % 10;
      x /= 10;
    }
    x = ans;
  }
  return x;
}
long long pw(long long a, long long b) {
  long long x = a;
  for (long long i = 1; i < b; i++) {
    a = a * x;
  }
  return a;
}
bool cmp(pair<long long, long long> a, pair<long long, long long> b) {
  return a.second < b.second;
}
long long solve() {
  long long n, k;
  cin >> n >> k;
  long long i = n - k;
  i /= 2;
  string s = "";
  for (long long j = 0; j < i; j++) s += '0';
  s += '1';
  long long x = 0;
  long long len = s.size();
  while (x < n) {
    cout << s[x % len];
    x++;
  }
  return 0;
}
signed main() {
  long long t = 1;
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin.exceptions(cin.failbit);
  clock_t time_req;
  time_req = clock();
  long long k = 1;
  while (t--) {
    solve();
  }
  time_req = clock() - time_req;
  return 0;
}
