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 in = new Scanner(System.in);
        int a = in.nextInt();
        int b = in.nextInt();
        int x = in.nextInt();
        if(x<2)
        {
            for(int i=0;i<b;i++)
                System.out.print("1");
            for(int i=0;i<a;i++)
                System.out.print("0");
        }
        else if(a>b)
        {
            int d = (x-1)/2;
            for(int i=0;i<d;i++)
            {
                System.out.print("01");
                a--;
                b--;
            }
            if((x-1)%2!=0)
            {
                System.out.print("0");
                a--;
                for(int i=0;i<b;i++)
                    System.out.print("1");
                for(int i=0;i<a;i++)
                    System.out.print("0");
            }
            else
            {
                for(int i=0;i<a;i++)
                    System.out.print("0");
                for(int i=0;i<b;i++)
                    System.out.print("1");
            }
        }
        else
        {
            int d = (x-1)/2;
            for(int i=0;i<d;i++)
            {
                System.out.print("10");
                a--;
                b--;
            }
            if((x-1)%2!=0)
            {
                System.out.print("1");
                b--;
                for(int i=0;i<a;i++)
                    System.out.print("0");
                for(int i=0;i<b;i++)
                    System.out.print("1");
            }
            else
            {
                for(int i=0;i<b;i++)
                    System.out.print("1");
                for(int i=0;i<a;i++)
                    System.out.print("0");
            }
//            for(int i=0;i<b;i++)
//                System.out.print("1");
//            for(int i=0;i<a;i++)
//                System.out.print("0");
        }
    }
}
