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 n, a, b, x, flag, minn, maxx, k = 0;
char m[205];
int main() {
  scanf("%d%d%d", &a, &b, &x);
  n = a + b;
  if (b >= a)
    flag = 1;
  else
    flag = 0;
  minn = min(a, b);
  maxx = max(a, b);
  if (x & 1 == 1) {
    x = (x + 1) / 2;
    for (int i = 1; i <= maxx - x; i++) {
      m[k++] = flag == 1 ? '1' : '0';
    }
    for (int i = 1; i <= x; i++) {
      m[k++] = flag == 1 ? '1' : '0';
      m[k++] = flag == 0 ? '1' : '0';
    }
    for (int i = 1; i <= minn - x; i++) {
      m[k++] = flag == 0 ? '1' : '0';
    }
  } else {
    x /= 2;
    for (int i = 1; i < maxx - x; i++) {
      m[k++] = flag == 1 ? '1' : '0';
    }
    for (int i = 1; i <= x; i++) {
      m[k++] = flag == 1 ? '1' : '0';
      m[k++] = flag == 0 ? '1' : '0';
    }
    for (int i = 1; i <= minn - x; i++) {
      m[k++] = flag == 0 ? '1' : '0';
    }
    m[k++] = flag == 1 ? '1' : '0';
  }
  printf("%s", m);
  return 0;
}
