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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int a = in.nextInt();
            int b = in.nextInt();
            int x = in.nextInt();
            StringBuilder sb = new StringBuilder();
            boolean flag = false;
            int length = a + b;
            while (length > 0) {
                sb.append("0");
                length--;
            }
            length = a + b - 1;
            int index = 0;
            // x =x-1;
            while (b > 0) {

                if (index != 0 && x == 2 && b < length - index) {
                    index++;
                    continue;
                }
                if (index == 0 && x % 2 == 0 && b < sb.length() - 1 && b < a) {
                    sb.setCharAt(++index, '1');
                    x = x - 1;
                } else if (index == 0 && x % 2 == 1) {
                    sb.setCharAt(index, '1');
                } else {
                    if (index != 0 && x >= 2) {
                        sb.setCharAt(++index, '1');
                    } else {
                        sb.setCharAt(index, '1');
                    }
                    if (index != 0 && sb.charAt(index - 1) == '0') {
                        x = x - 2;
                    }
                }

                index++;
                b--;
            }
            out.print(sb.toString());
        }

    }
}

