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

public class Solution {
    static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args)throws IOException {
        String S[] = in.readLine().split(" ");
        int a, b, x, c, i;
        a = Integer.parseInt(S[0]);
        b = Integer.parseInt(S[1]);
        x = Integer.parseInt(S[2]);
        String s = "";
        c = (a>b)?0:1;
        for(i=0; i<x-1; i++) {
            if(c == 0) {
                s = s + "0";
                c = 1;
                a--;
            }
            else {
                s = s + "1";
                c = 0;
                b--;
            }
        }
        if(i >= 1) {
            if (s.charAt(i - 1) == '0') {
                while (b > 0) {
                    s = s + "1";
                    b--;
                }
                while (a > 0) {
                    s = s + "0";
                    a--;
                }
            } else {
                while (a > 0) {
                    s = s + "0";
                    a--;
                }
                while (b > 0) {
                    s = s + "1";
                    b--;
                }
            }
        }
        else {
            while (b > 0) {
                s = s + "1";
                b--;
            }
            while (a > 0) {
                s = s + "0";
                a--;
            }
        }
        System.out.print(s);
    }
}
