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 intcmp(const void *v1, const void *v2) { return *(int *)v1 - *(int *)v2; }
int a, b, x;
int main() {
  string s = "";
  cin >> a >> b >> x;
  int expanda = a - x / 2;
  int expandb = b - x / 2;
  if (x % 2 != 1) {
    if (a > b) {
      s = "0";
      for (int i = 0; i < x / 2; i++) {
        s += "10";
      }
      expanda--;
    } else {
      s = "1";
      for (int i = 0; i < x / 2; i++) {
        s += "01";
      }
      expandb--;
    }
  } else {
    for (int i = 0; i < (x + 1) / 2; i++) {
      s += "01";
    }
    expanda--;
    expandb--;
  }
  int len = s.length();
  for (int i = 0; i < len; i++) {
    while (expanda != 0 && s[i] == '0') {
      cout << "0";
      expanda--;
    }
    while (expandb != 0 && s[i] == '1') {
      cout << "1";
      expandb--;
    }
    cout << s[i];
  }
  while (expanda != 0) {
    cout << "0";
    expanda--;
  }
  while (expandb != 0) {
    cout << "1";
    expandb--;
  }
  cout << endl;
  return 0;
}
