You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).

Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.

Input

The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).

Output

Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.

Examples

Input

2 2 1


Output

1100


Input

3 3 3


Output

101100


Input

5 3 6


Output

01010100

Note

All possible answers for the first example: 

  * 1100; 
  * 0011. 



All possible answers for the second example: 

  * 110100; 
  * 101100; 
  * 110010; 
  * 100110; 
  * 011001; 
  * 001101; 
  * 010011; 
  * 001011. 
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, i, k, j, ans = 0, m, w, mx = 0, l, r, x, y, r1, c1, r2, c2, t;
  cin >> n >> x >> y;
  m = min(n, x);
  string s;
  s = "";
  if (y > m) {
    if (n > x) {
      for (i = 0; i < (y + 1); i++) {
        if (i % 2 == 0) {
          s += '0';
          n--;
        } else {
          s += '1';
          x--;
        }
      }
      for (i = 0; i < n; i++) cout << '0';
      for (i = 0; i < s.length(); i++) {
        if (s[i] == '1' && ans == 0) {
          ans = 1;
          cout << s[i];
          for (j = 0; j < x; j++) cout << '1';
        } else
          cout << s[i];
      }
    } else {
      for (i = 0; i < (y + 1); i++) {
        if (i % 2 == 0) {
          s += '1';
          x--;
        } else {
          s += '0';
          n--;
        }
      }
      for (i = 0; i < x; i++) cout << '1';
      for (i = 0; i < s.length(); i++) {
        if (s[i] == '0' && ans == 0) {
          ans = 1;
          cout << s[i];
          for (j = 0; j < n; j++) cout << '0';
        } else
          cout << s[i];
      }
    }
  } else {
    for (i = 0; i < (y + 1); i++) {
      if (i % 2 == 0) {
        s += '0';
        n--;
      } else {
        s += '1';
        x--;
      }
    }
    for (i = 0; i < n; i++) cout << '0';
    for (i = 0; i < s.length(); i++) {
      if (s[i] == '1' && ans == 0) {
        ans = 1;
        cout << s[i];
        for (j = 0; j < x; j++) cout << '1';
      } else
        cout << s[i];
    }
  }
}
