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.ArrayList;
import java.util.Comparator;
import java.util.Scanner;
import java.util.SortedSet;

public class B {

    public static void main(String args[]) {
        new B().run();
    }

    void run() {
        Scanner s = new Scanner(System.in);
        int a = s.nextInt(), b = s.nextInt(), x = s.nextInt();
        String r = "";
        String z0 = "0";
        String z1 = "1";
        if(b>a){
            int sb=b;b=a;a=sb;
            z0="1";
            z1="0";
        }
        boolean z = true;
        if (x > 1) {
            r += z0;
            a--;
            z = false;
            while (x > 2) {
                x--;
                if (z) {
                    r += z0;
                    a--;
                    z = false;
                } else {
                    r += z1;
                    b--;
                    z = true;
                }
            }
        }
        if (z) {
            while (a > 0) {

                r += z0;
                a--;
            }
        }
        while (b > 0) {

            r +=z1;
            b--;
        }
        while (a > 0) {

            r += z0;
            a--;
        }
        System.out.println(r);
    }
}
