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.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintStream;
import java.util.PriorityQueue;
import java.util.Scanner;

/**
 * Copyright © 2018 Chris. All rights reserved.
 *
 * @author Chris
 * 2018/7/1 22:23
 * @see CFR493.div2
 */
public class Main {

    private static void solve(Scanner sc) {
        int a = sc.nextInt();
        int b = sc.nextInt();
        int x = sc.nextInt();

        int n = a + b;

        int ans[] = new int[n];

        if (b >= a) {
            for (int i = 0; i < b; i++) {
                ans[i] = 1;
            }
            x--;
            int k = 1;
            if (x % 2 == 1) {
                ans[b - 1] = 0;
                ans[n - k] = 1;
                k++;
                x--;
                b--;
            }

            k++;
            while (x > 0) {
                ans[b - 1] = 0;
                ans[n - k] = 1;
                k += 2;
                x -= 2;
                b -= 1;
            }
        } else {
            for (int i = a; i < n; i++) {
                ans[i] = 1;
            }
            x--;
            int k = 1;
            if (x % 2 == 1) {
                ans[a - 1] = 1;
                ans[n - k] = 0;
                k++;
                x--;
                a--;
            }

            k++;
            while (x > 0) {
                ans[a - 1] = 1;
                ans[n - k] = 0;
                k += 2;
                x -= 2;
                a -= 1;
            }
        }

        for (int i = 0; i < n; i++) {
            System.out.print(ans[i]);
        }
    }

    public static void main(String args[]) throws FileNotFoundException {
        //System.setIn(new FileInputStream("in.txt"));
        //System.setOut(new PrintStream("out.txt"));

        solve(new Scanner(System.in));
    }
}
