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 B;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class B1003_BinaryStringConstructing {

    public static void main(String[] args) throws IOException {
        int zeroCount;
        int oneCount;
        int indexCount;
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            String[] numbers = br.readLine().split(" ");
            zeroCount = Integer.parseInt(numbers[0]);
            oneCount = Integer.parseInt(numbers[1]);
            indexCount = Integer.parseInt(numbers[2]);
        }
        int mainSecSize = (indexCount + 1) / 2;
        StringBuilder sb = new StringBuilder();
        if (indexCount % 2 == 0) {
            if (zeroCount < oneCount) {
                String main = "10";
                for (int i = 0; i < mainSecSize; i++) {
                    sb.append(main);
                }
                for (int i = 0; i < zeroCount - mainSecSize; i++) {
                    sb.append("0");
                }
                sb.append("1");
                for (int i = 0; i < oneCount - mainSecSize - 1; i++) {
                    sb.append("1");
                }
            } else {
                String main = "01";
                for (int i = 0; i < zeroCount - mainSecSize - 1; i++) {
                    sb.append("0");
                }
                for (int i = 0; i < mainSecSize; i++) {
                    sb.append(main);
                }
                for (int i = 0; i < oneCount - mainSecSize; i++) {
                    sb.append("1");
                }
                sb.append("0");
            }
        } else {
            if (zeroCount < oneCount) {
                String main = "10";
                for (int i = 0; i < oneCount - mainSecSize; i++) {
                    sb.append("1");
                }
                for (int i = 0; i < mainSecSize; i++) {
                    sb.append(main);
                }
                for (int i = 0; i < zeroCount - mainSecSize; i++) {
                    sb.append("0");
                }
            } else {
                String main = "01";
                for (int i = 0; i < zeroCount - mainSecSize; i++) {
                    sb.append("0");
                }
                for (int i = 0; i < mainSecSize; i++) {
                    sb.append(main);
                }
                for (int i = 0; i < oneCount - mainSecSize; i++) {
                    sb.append("1");
                }
            }
        }
        System.out.println(sb.toString());
    }
}
