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;
const int INFTY = 20000000;
const int MAX = 500100;
const int MOD = 10000000;
void coutTab(int* tab, int n) {
  for (int i = 0; i < n; i++) {
    cout << tab[i] << " ";
  }
  cout << "\n";
}
string create(int a, int b, int x, int start) {
  if (start == 0)
    a--;
  else
    b--;
  string s;
  s.push_back(start + '0');
  char l;
  for (int i = 0; i < x - 1; i++) {
    l = s[s.size() - 1];
    if (l == '1') {
      s.push_back('0');
      a--;
    } else {
      s.push_back('1');
      b--;
    }
  }
  l = s[s.size() - 1];
  if (l == '0') {
    while (a--) s.push_back('0');
    while (b--) s.push_back('1');
  } else {
    while (b--) s.push_back('1');
    while (a--) s.push_back('0');
  }
  return s;
}
bool check(string s, int x) {
  int j = 0;
  for (int i = 1; i < s.size(); i++) {
    if (s[i - 1] != s[i]) j++;
  }
  return x == j;
}
int main() {
  ios_base::sync_with_stdio(0);
  int a, b, x;
  cin >> a >> b >> x;
  string res = create(a, b, x, 0);
  if (!check(res, x)) res = create(a, b, x, 1);
  cout << res << "\n";
}
