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.*;
import java.io.*;

public class B1003 
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int a = in.nextInt();
		int b = in.nextInt();
		int x = in.nextInt();
		int max=0,min=0;
		char[] ans = new char[a+b];
		
		char s,e;
		
		if(a>b)
		{
			s = '0';
			e = '1';
			max = a;
			min = b;
		}
		else
		{
			s = '1';
			e = '0';
			max = b;
			min = a;
		}
		
		int i=0,r = a + b - x;
		
		while(x>0)
		{
			if(i%2==0)
			{
				ans[i] = s;
				max--;
			}
			else
			{
				ans[i] = e;
				min--;
			}
			
			x--;
			i++;
		}
		
		if(i!=0 && ans[i-1]==s)
		{
			while(max>0)
			{
				ans[i] = s;
				i++;
				max--;
			}
			
			while(min>0)
			{
				ans[i] = e;
				i++;
				min--;
			}
		}
		else
		{
				while(min>0)
				{
					ans[i] = e;
					i++;
					min--;
				}
			
				while(max>0)
				{
					ans[i] = s;
					i++;
					max--;
				}
		}
		
		for(int j=0;j<a+b;j++)
			System.out.print(ans[j]);
	}

}
