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. 
// https://codeforces.com/contest/260/submission/68336826

import java.math.*;
import java.util.*;
import java.io.*;
  
public class B { 
  
    static BufferedReader in;
    static String file = "../in";

    public static void main(String[] args) throws Exception
    {
        int test = 10,   // 0 for local testing, 1 for std input
            _k = Integer.valueOf("1");
        if(test > 0) in = new BufferedReader(new InputStreamReader(System.in));
        else in = new BufferedReader(new FileReader(file));
        if(test < 0) {String[] str = in.readLine().split(" ");}
        
        /****************************************************/
        /****************************************************/
        /****************************************************/
        /****************************************************/

        // int n = Integer.valueOf(in.readLine());
        String[] sp = in.readLine().split(" ");
        String astr = sp[0];
        int a = Integer.valueOf(sp[0]),
            b = Integer.valueOf(sp[1]),
            k = Integer.valueOf(sp[2]);
        // k indices where the consecutive indices are different
        String str = "";
        int start = 1;
        if(a > b) start = 0;
        while(k-- > 1) {
            if(start == 0) {
                str += "0";
                a--;
            }
            else {
                str += "1";
                b--;
            }
            start = 1 - start;
        }
        if(start == 0) {
            while(a-- > 0) str += "0";
            while(b-- > 0) str += "1";
        }
        else {
            while(b-- > 0) str += "1";
            while(a-- > 0) str += "0";
        }

        System.out.println(str);

    }
}