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.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt(); int b = sc.nextInt(); int x = sc.nextInt();
        sc.nextLine();
        StringBuilder sb = new StringBuilder();

        if(a == 1 && x == 2) {
            sb.append(1);
            sb.append(0);
            for (int i = 0; i < b - 1; i++) {
                sb.append(1);
            }

            System.out.println(sb.toString());
            System.exit(0);
        }

        if (b == 1 && x == 2) {
            sb.append(0);
            sb.append(1);
            for (int i = 0; i < a - 1; i++){
                sb.append(0);
            }

            System.out.println(sb.toString());
            System.exit(0);
        }



        if (x == 1) {
            for (int i = 0; i < a; i++) {
                sb.append("0");
            }

            for (int i = 0; i < b; i++) {
                sb.append("1");
            }
            System.out.println(sb.toString());
            System.exit(0);

        } else {
            if (x %2 == 0) {
                if (a > b) {
                    for (int i = 0; i < x / 2; i++) {
                        sb.append(0);
                        sb.append(1);
                    }

                    for (int i = 0; i < b - (x / 2); i++) {
                        sb.append(1);
                    }

                    for (int i = 0; i < a - (x / 2); i++) {
                        sb.append(0);
                    }
                }

                if (a <= b) {
                    for (int i = 0; i < x / 2; i++) {
                        sb.append(1);
                        sb.append(0);
                    }

                    for (int i = 0; i < a - (x / 2); i++) {
                        sb.append(0);
                    }

                    for (int i = 0; i < b - (x / 2); i++) {
                        sb.append(1);
                    }
                }
            } else {
                if (a > b) {
                    for (int i = 0; i < x / 2; i++) {
                        sb.append(0);
                        sb.append(1);
                    }

                    for (int i = 0; i < a - (x / 2); i++) {
                        sb.append(0);
                    }

                    for (int i = 0; i < b - (x / 2); i++) {
                        sb.append(1);
                    }
                }

                if (a <= b) {
                    for (int i = 0; i < x / 2; i++) {
                        sb.append(1);
                        sb.append(0);
                    }

                    for (int i = 0; i < b - (x / 2); i++) {
                        sb.append(1);
                    }

                    for (int i = 0; i < a - (x / 2); i++) {
                        sb.append(0);
                    }

                }
            }
        }


        System.out.println(sb.toString());
    }


}