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.*;
import java.util.*;

public class mymy
{
	public static void main(String[] Rohan)throws IOException
	{
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

		
		String[] s=br.readLine().split(" ");
		int z=Integer.parseInt(s[0]),o=Integer.parseInt(s[1]),x=Integer.parseInt(s[2]);
		
		char[] c=new char[z+o];
		int i=0,l=z+o;
		if(x==1)
		{
			while(o>0)
			{
				c[i]='1';
				o--;i++;
			}
			while(z>0)
			{
				c[i]='0';
				z--;i++;
			}
		}
		else
		{
			if(o>z)
			{
				c[0]='1';i=1;o--;
			while(x>1&&i<l)
			{
				if(i%2==0)
				{
					c[i]='1';i++;o--;
					x--;
				}
				else
				{
					c[i]='0';i++;z--;x--;
				}
			}	
			}
			else
			{
			c[0]='0';i=1;z--;
			while(x>1&&i<l)
			{
				if(i%2==0)
				{
					c[i]='0';i++;z--;
					x--;
				}
				else
				{
					c[i]='1';i++;o--;x--;
				}
			}
			}
			
			if(c[i-1]=='0')
			{
				while(z>0)
				{
					c[i]='0';i++;z--;
				}
				
				while(o>0)
				{
					c[i]='1';i++;o--;
				}
			}
			else
			{
				while(o>0)
				{
					c[i]='1';i++;o--;
				}
				while(z>0)
				{
					c[i]='0';i++;z--;
				}

			}
		}
		for(int i1=0;i1<l;i1++)
			System.out.print(c[i1]+"");
		System.out.println();
		
		
	}
}

