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 com.company;

import java.io.*;

public class Main
{
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        StringBuilder outputString = new StringBuilder();

        String data[] = br.readLine().split(" ");

        int a = Integer.parseInt(data[0]);
        int b = Integer.parseInt(data[1]);
        int x = Integer.parseInt(data[2]);

        String result = "";

        if(x == 1)
        {
            while(a-->0)
            {
                result += "0";
            }

            while(b-->0)
            {
                result += "1";
            }
        }
        else
        {
            result += "01";

            a--;
            b--;
            x--;

            boolean zero = true;

            while(x > 0)
            {
                if(zero)
                {
                    if(a == 0)
                        break;

                    result += "0";
                    zero = false;
                    a--;
                }
                else
                {
                    if(b == 0)
                        break;

                    result += "1";
                    zero = true;
                    b--;
                }

                x--;
            }

            if(x != 0)
            {
                if(result.length()%2 == 0)
                {
                    result = "1" + result;
                    b--;
                }

                x--;
            }

            if(x == 0)
            {
                if(result.length()%2 == 0)
                {
                    while(a-->0)
                    {
                        result = "0" + result;
                    }

                    while(b-->0)
                    {
                        result = result + "1";
                    }
                }
                else
                {
                    while(a-->0)
                    {
                        result = "0" + result;
                    }

                    String temp = "";

                    while(b-->0)
                    {
                        temp = temp + "1";
                    }

                    String newString = result.substring(0,result.length()-1) + temp + result.charAt(result.length()-1);

                    result = newString;
                }
            }
            else
            {

            }
        }

        outputString.append(result).append("\n");

        bw.write(outputString.toString());
        bw.close();
    }
}
