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. 
import java.io.*;
import java.util.*;

public class CF_binarystringconstructing {
  public static void main (String [] args) throws IOException {
    PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
    Scanner sc = new Scanner(System.in);//new File("input.txt"));
    
    int a = sc.nextInt();
    int b = sc.nextInt();
    int s = sc.nextInt();

    int p = a+b;

    String as = "0";
    String bs = "1";

    if(a<b){
      int temp = a;
      a = b;
      b = temp;
      as = "1";
      bs = "0";
    }

    String t = as;
    a--;

    for(int i = 0; i < p; i++){
      if(s > 1){
        if(t.substring(t.length()-1).equals(as)){
          t += bs;
          b--;
        }else{
          t += as;
          a--;
        }
        s--;
      }else{
        if(t.substring(t.length()-1).equals(as)){
          if(a>0){
            t += as;
            a--;
          }else{
            t+=bs;
            b--;
          }
        }else{
          if(b>0){
            t += bs;
            b--;
          }else{
            t+=as;
            a--;
          }
        }
      }
    }
    t = t.substring(0, t.length()-1);
    System.out.println(t);
    out.println(t);                           // output result
    out.close();                                  // close the output file
    sc.close();
  }
  
}