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.io.*;
import java.util.*;
public class Q1 {
    public static void main(String[] args) throws Exception{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter w=new PrintWriter(System.out);
        int i,j,a,b,x,n;
        String ans="";
        String s[]=br.readLine().split(" ");
        a=Integer.parseInt(s[0]);
        b=Integer.parseInt(s[1]);
        x=Integer.parseInt(s[2]);
        if(a>b)n=0;
        else n=1;
        for(i=0;i<=x;i++){
            ans+=n;
            if(n==0) a--;
            else b--;
            n^=1;
        }
        for(i=0;i<ans.length();i++){
            w.print(ans.charAt(i));
            if(ans.charAt(i)=='0' && a>0){
                for(j=0;j<a;j++){
                    w.print(ans.charAt(i));
                }
                a=0;
            }
            else if(ans.charAt(i)=='1' && b>0){
                for(j=0;j<b;j++){
                    w.print(ans.charAt(i));
                }
                b=0;
            }
        }
        w.flush();
        w.close();
    }
}