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. 
// package cf1003;

import java.io.BufferedInputStream;
import java.util.Scanner;

public class Main {
    static Scanner in = new Scanner(new BufferedInputStream(System.in));
    static public void main(String argv[]){
        while(in.hasNext()){
            int a0 = in.nextInt();
            int b1 = in.nextInt();
            int n  = in.nextInt();
            String prefix = "";
            if(a0>=b1){
                for(int i=0;i<n;i++){
                    if(i%2==0){
                        prefix+="0";
                        a0--;
                    }else{
                        prefix+="1";
                        b1--;
                    }
                }
                String mid ="";
                String suffer = "";
                if(n%2==0){
                    while(b1>0){
                        mid+="1";
                        b1--;
                    }
                    while(a0>0){
                        mid+="0";
                        a0--;
                    }
                }else{
                    while(a0>0){
                        mid+="0";
                        a0--;
                    }
                    while(b1>0){
                        suffer+="1";
                        b1--;
                    }
                }
                System.out.println(prefix+mid+suffer);
            }else{
                for(int i=0;i<n;i++){
                    if(i%2==0){
                        prefix+="1";
                        b1--;
                    }else{
                        prefix+="0";
                        a0--;
                    }
                }
                String mid = "";
                String suffer ="";
                if(n%2==0){
                    while(a0>0){
                        mid+="0";
                        a0--;
                    }
                    while(b1>0){
                        suffer+="1";
                        b1--;
                    }
                }else{
                    while(b1>0){
                        mid+="1";
                        b1--;
                    }
                    while(a0>0){
                        suffer+="0";
                        a0--;
                    }
                }
                System.out.println(prefix+mid+suffer);
            }
        }
    }
}
