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 whatever //do not write package name here */

import java.io.*;
import java.util.*;
public class GFG {
	public static void main (String[] args) {
		//System.out.println("GfG!");
		Scanner sc=new Scanner(System.in);
		int a=sc.nextInt();
		int b=sc.nextInt();
		int x=sc.nextInt();
		String s="";
		if(a>b){
		    s=s+"0";
		    a--;
		}
	    else{
	        s=s+"1";
	        b--;
	    }
	    int len=1;
	    while(x>1){
	        if(s.charAt(s.length()-1)=='0'){
	            s=s+"1";
	            b--;
	        }
	        else{    
	            s=s+"0";
	            a--;
	        }
	        len++;
	        x--;
	    }
	    if(s.charAt(s.length()-1)=='0'){
	        while(a>0){
	            s=s+"0";
	            a--;
	        }
	        while(b>0){
	            s=s+"1";
	            b--;
	        }
	    }
	    else if(s.charAt(s.length()-1)=='1'){
	        while(b>0){
	            s=s+"1";
	            b--;
	        }
	        while(a>0){
	            s=s+"0";
	            a--;
	        }
	    }
	    System.out.println(s);
	}
}