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.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main{
    public static void main(String[] args)throws IOException{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	PrintWriter out = new PrintWriter(System.out);
	String pp[] = br.readLine().split(" ");
	int a = Integer.parseInt(pp[0]);
	int b = Integer.parseInt(pp[1]);
	int x = Integer.parseInt(pp[2]);
	int p = 0;
	int c[] = new int[2];
	c[0] = a;
	c[1] = b;
	boolean f = a>b;
	String ans = "";
	if(a>b){
	    ans = "0";
	    p = 1;
	    c[0]--;
	}else{
	    ans = "1";
	    p = 0;
	    c[1]--;
	}
	int l = x;
	while(x>0){
	    ans+=""+p;
	    c[p]--;
	    p^=1;
	    x--;
	}
	String one = "";
	String z = "";
	while(c[0]>0){
	    z+="0";
	    c[0]--;
	}
	while(c[1]>0){
	    one+="1";
	    c[1]--;
	}
	if(l%2==0){
	    String aux = ans.substring(0,ans.length()-1);
	    if(f){
		out.println(z+aux+one+"0");
	    }else{
		out.println(one+aux+z+"1");
	    }
	}else{
	    String aux = ans.substring(0,ans.length()-1);
	    if(f){
		out.println(aux+z+one+"1");
	    }else{
		out.println(aux+one+z+"0");
	    }
	}

	out.close();
    }
}
