#include <bits/stdc++.h>
using namespace std;
long long n, m, ans, mid, mn, mx, T, sum, h1, h2, e[1234567], b[1234567],
    c[1234567], d[1 << 20], k, i, j, l, r, h, a[1234567], w, x, y, z, res,
    par[1234567], cnt, sz[1234567];
bool used[1234567];
vector<long long> v[1234567], vec1;
string s1, s;
vector<pair<long long, long long> > vp[1234567];
bool ok;
long long cc[323456][30];
long long dx[4] = {0, 0, 1, -1}, dy[4] = {1, -1, 0, 0};
char cha[4] = {'R', 'L', 'D', 'U'};
set<long long> st;
char ch[1234][2345];
long long vis[1235][1234];
long long xx, yy;
vector<long long> vec;
map<pair<long long, long long>, long long> mp;
int main() {
  cin >> n >> k;
  cnt = (n - k) / 2;
  for (long long i = 1; i <= n; i++) cout << !(i % (cnt + 1));
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
long long n, m, ans, mid, mn, mx, T, sum, h1, h2, e[1234567], b[1234567],
    c[1234567], d[1 << 20], k, i, j, l, r, h, a[1234567], w, x, y, z, res,
    par[1234567], cnt, sz[1234567];
bool used[1234567];
vector<long long> v[1234567], vec1;
string s1, s;
vector<pair<long long, long long> > vp[1234567];
bool ok;
long long cc[323456][30];
long long dx[4] = {0, 0, 1, -1}, dy[4] = {1, -1, 0, 0};
char cha[4] = {'R', 'L', 'D', 'U'};
set<long long> st;
char ch[1234][2345];
long long vis[1235][1234];
long long xx, yy;
vector<long long> vec;
map<pair<long long, long long>, long long> mp;
int main() {
  cin >> n >> k;
  cnt = (n - k) / 2;
  for (long long i = 1; i <= n; i++) cout << !(i % (cnt + 1));
}

```