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.Scanner;
public class Main {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
        int zero = s.nextInt();
        int one = s.nextInt();
        int x = s.nextInt();
        StringBuilder sb = new StringBuilder();
        if(zero >= one){
            sb.append('0');
            zero--;
            while(x >= 2 && one > 0 && zero > 0){
                sb.append("10");
                one--;
                zero--;
                x = x - 2;
            }
          if(x == 1){
            while(zero > 0){
                sb.append('0');
                zero--;
            }
            while(one > 0){
                sb.append('1');
                one--;
            }
          }
          else{
              sb.deleteCharAt(sb.length() - 1);
              zero++;
              while(one > 0){
                sb.append('1');
                one--;
             }
            while(zero > 0){
                sb.append('0');
                zero--;
            }
          }
            
        }
        else{
            sb.append('1');
            one--;
            while(x >= 2 && one > 0 && zero > 0){
                sb.append("01");
                one--;
                zero--;
                x = x - 2;
            }
            if(x == 1){
            while(one > 0){
                sb.append('1');
                one--;
            }
            while(zero > 0){
                sb.append('0');
                zero--;
            }
            }
            else{
                sb.deleteCharAt(sb.length() - 1);
                one++;
                while(zero > 0){
                sb.append('0');
                zero--;
            }
              while(one > 0){
                sb.append('1');
                one--;
            }

            }
        }
        System.out.println(sb);
       
        
        
    }
}