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.util.*;
public class b{
    public static String make(int h,char o, int l,char y, int x){
        StringBuilder sb = new StringBuilder("");
        int i=0;
        boolean check=true;
        while (i<x+1){
            if (check){
                sb.append(o);
                h--;
                i++;
            }else{
                sb.append(y);
                l--;
                i++;
            }
            check = !check;
        }
        while (h>0){
            for ( i=0; i< sb.length();i++){
                if (sb.charAt(i) == o){
                    sb.insert(i,o);
                    h--;
                    break;
                }
            }
        }
        while (l>0){
            for ( i=0; i< sb.length();i++){
                if (sb.charAt(i) == y){
                    sb.insert(i,y);
                    l--;
                    break;
                }
            }
        }
        return sb.toString();
    }
    public static void main(String argv[]){
        Scanner input = new Scanner(System.in);
        int a = input.nextInt();
        int b = input.nextInt();
        int x = input.nextInt();
        
        if (a>b){
            System.out.print(make(a,'0',b,'1',x));
        }else{
            System.out.print(make(b,'1',a,'0',x));
        }
    }
}