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.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class contest {static int zeroc,onec;


	public static void main(String[] args) {
		// TODO Auto-generated method stub
Scanner in=new Scanner(System.in);
ArrayList <Integer> list=new ArrayList<Integer>();
int zero=in.nextInt();String str;
int one=in.nextInt();
int x=in.nextInt();
if(zero>one)
{	str="01";String s2="";
 for(int i=0;i<x-1;i++)
 {
	 if(i%2==0)
	 { s2+="0";zeroc++;}
	 else
		 {s2+="1";onec++;}
 }
 zero=zero-zeroc-1;
 one=one-onec-1;
 String s1="";
 while(one-->0)
 {s1+="1";}
 str=str+s1+s2;
 String s = "";
 while(zero-->0)
 {s+="0";}
 str=s+str;
 
System.out.println(str);

}
else
	{str="10";String s2="";
	 for(int i=0;i<x-1;i++)
	 {
		 if(i%2==0)
		 { s2+="1";onec++;}
		 else
			 {s2+="0";zeroc++;}
	 }
	 zero=zero-zeroc-1;
	 one=one-onec-1;
	 String s = "";
	 while(zero-->0)
	 {s+="0";}
	 str=str+s+s2;;
	 String s1="";
	 while(one-->0)
	 {s1+="1";}
	 str=s1+str;;
	
	 
	System.out.println(str);}

	

	}

}
