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;
long long BE(int a, int b) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) {
      res = (res * a);
    }
    a = a * a;
    b = b >> 1;
  }
  return res;
}
void pro() {
  bool ok = 0;
  string second;
  long long n, k, m;
  cin >> n >> m >> k;
  long long h = n, l = m;
  long long p = -1;
  char first, c;
  if (m > n)
    first = '1', c = '0', h = m, l = n, ok = 1;
  else
    first = '0', c = '1';
  while (p != k - 1) {
    if (p & 1)
      second += first, h--;
    else
      second += c, l--;
    p++;
  }
  char g = second[p];
  if (g == '0') {
    if (ok) swap(h, l);
    for (long long i = p + 1; i < n + m; i++) {
      if (h != 0) {
        second += '0';
        h--;
      } else if (l != 0)
        second += '1';
    }
  } else {
    if (ok) swap(h, l);
    for (long long i = p + 1; i < n + m; i++) {
      if (l != 0)
        second += '1', l--;
      else if (h != 0)
        second += '0';
    }
  }
  cout << second << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  pro();
}
