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.*;
public class B1003 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a =sc.nextInt();
        int b = sc.nextInt();
        int x = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        if (a >= b) {
            sb.append('0');
            a--;
        } else {
            sb.append('1');
            b--;
        }
        
        while (x > 1) {
            if (sb.charAt(sb.length()-1) == '1') {
                sb.append('0');
                a--;
            } else {
                sb.append('1');
                b--;
            }
            x--;
        }
        if (sb.charAt(sb.length()-1) == '0') {
            while (a > 0) {
                a--;
                sb.append('0');
            }
            while (b > 0) {
                b--;
                sb.append('1');
            }
        } else {
            while (b > 0) {
                b--;
                sb.append('1');
            }
            while (a > 0) {
                a--;
                sb.append('0');
            }
        }
        System.out.println(sb.toString());
    }
}