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.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int b = sc.nextInt();//0
        int a = sc.nextInt();
        int x = sc.nextInt();
        int n = a + b;
        char[] s = new char[n];
        int i = 0;
        boolean f = true;
        char tt = 0;
        if (a < b) {
            f = !f;
        }
        while (x-- > 0) {
            tt = f ? '1' : '0';
            s[i++] = tt;
            f = !f;
        }
        for (i = 0; i < n; i++) {
            if (s[i] == '1') {
                a--;
                continue;
            }
            if (s[i] == '0') {
                b--;
                continue;
            }
            if (tt == '1') {
                if (a > 0) {
                    s[i] = '1';
                    a--;
                    continue;
                }
                if (a == 0) {
                    tt = '0';
                    s[i] = '0';
                    b--;
                    continue;
                }
            }
            if (tt == '0') {
                if (b > 0) {
                    s[i] = '0';
                    b--;
                    continue;
                }
                if (b == 0) {
                    tt = '1';
                    s[i] = '1';
                    a--;
                    continue;
                }
            }




        }
        System.out.println(String.valueOf(s));
    }
}
