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.lang.reflect.Array;
import java.util.*;
public class B {
    public static void main(String[] args) throws IOException
    {
        new B().run();
    }

    StreamTokenizer in;
    PrintWriter out;


    int nextInt() throws IOException
    {
        in.nextToken();
        return (int)in.nval;
    }
    String nextString() throws IOException{
        in.nextToken();
        return in.sval;
    }

    void run() throws IOException
    {
        in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    void solve() throws IOException
    {
        int a = nextInt();
        int b = nextInt();
        int x = nextInt();
        boolean flag = a<b ? true:false;
//        System.out.println(flag);
        int len = a + b;
        for(int i = 1; i<= len; i++){
                if(flag){
                    b--;
                    System.out.print("1");
                }else{
                    a--;
                    System.out.print("0");
                }
                if(x>1){
                    flag = !flag;
                    x--;
                }
                else if (x == 1){
                    if(a==0||b==0){
                        x--;
                        flag=!flag;
                    }
                }
        }
    }
}
