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 N = 1010;
const int dir[4][2] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
int GCD(int a, int b) { return b ? GCD(b, a % b) : a; }
int main() {
  int i, b, j, k, x, a, l;
  cin >> a >> b >> x;
  if (a > b) {
    int flag = 0;
    while (x > 2) {
      if (flag == 0) {
        printf("01");
        a--;
        b--;
        x--;
        flag = 1;
        continue;
      }
      printf("01");
      a--;
      b--;
      x -= 2;
    }
    if (x == 2) {
      if (flag == 0) {
        printf("01");
        a--;
        b--;
        for (i = 0; i < b; i++) printf("1");
        for (i = 0; i < a; i++) printf("0");
      } else {
        for (i = 0; i < a; i++) printf("0");
        for (i = 0; i < b; i++) printf("1");
      }
    }
    if (x == 1) {
      for (i = 0; i < b; i++) printf("1");
      for (i = 0; i < a; i++) printf("0");
    }
  } else {
    int flag = 0;
    while (x > 2) {
      if (flag == 0) {
        printf("10");
        a--;
        b--;
        x--;
        flag = 1;
        continue;
      }
      printf("10");
      a--;
      b--;
      x -= 2;
    }
    if (x == 1) {
      for (i = 0; i < a; i++) printf("0");
      for (i = 0; i < b; i++) printf("1");
    }
    if (x == 2) {
      if (flag == 0) {
        printf("10");
        a--;
        b--;
        for (i = 0; i < a; i++) printf("0");
        for (i = 0; i < b; i++) printf("1");
      } else {
        for (i = 0; i < b; i++) printf("1");
        for (i = 0; i < a; i++) printf("0");
      }
    }
  }
  printf("\n");
  return 0;
}
