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.Scanner;

public class afsaf {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		int x = sc.nextInt();
		StringBuffer s  = new StringBuffer();
		boolean flip = false;
		int a1 = a;
		int b1 = b;
		if(a>b){
			flip=true;
		}else{
			flip=false;
		}
		for(int i=0;i<x+1;i++){
			if(flip){
				s.append(0);
				a--;
			}else{
				s.append(1);
				b--;
			}
			flip=!flip;
		}
		String res = s.toString();
//		System.out.println(a+" "+b);
//		System.out.println(res);
		if(a>0){
			StringBuffer s1 = new StringBuffer();
			
			while(a-->0){
				s1.append(0);
			}
			if(a1>b1){
				res = s1.toString()+res;
				
			}else{
				res = "1"+s1.toString()+res.substring(1);
				
			}
		}
//		System.out.println(res);
		if(b>0){
			StringBuffer s2 = new StringBuffer();
			while(b-->0){
				s2.append(1);
			}
			for(int i=0;i<res.length();i++){
				if(res.charAt(i)=='1'){
					res = res.substring(0,i+1)+s2.toString()+res.substring(i+1);
					break;
				}
			}
			
			
		}
		System.out.println(res);
		

	}

}
