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;
import java.util.Arrays;
import java.lang.Math;

public class Demo{
	static Scanner in = new Scanner(System.in);
    public static void main(String[] args) {
        int N = in.nextInt();
        int M = in.nextInt();
        int x = in.nextInt();
        int flag = 0,cn = 0,cm = 0;
        if(N > M && x != 1){
        	flag = 1;
        }
        for(int i = 1; i < x; i++){
        	if(flag == 0){
        		System.out.print(1);
        		flag = 1;
        		cn++;
        	}
        	else{
        		System.out.print(0);
        		flag = 0;
        		cm++;
        	}
        }
        if(flag == 0){
    		for(int i = cn; i < M; i++){
    			System.out.print(1);
    		}
    		for(int i = cm; i < N; i++){
    			System.out.print(0);
    		}
    	}
    	else{
    		for(int i = cm; i < N; i++){
    			System.out.print(0);
    		}
    		for(int i = cn; i < M; i++){
    			System.out.print(1);
    		}
    	}
   	}
}  