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;
//codeforces.com/problemset/problem/1003/B
public class Class1 {
	public static void main(String[] args) {
		Scanner input=new Scanner(System.in);
		int a=input.nextInt();
		int b=input.nextInt();
		int x=input.nextInt();
		int n=a+b;
		int[] result=new int[n];
		int counter=0,dif=0;
		if(a>=b) {
			for(int i=0;i<x+1;i++) 
				result[i]=i%2;
			for(int i=x+1;i<n;i++)
				result[i]=result[x];
		}
		else {
			for(int i=0;i<x+1;i++) 
				result[i]=(i+1)%2;
			for(int i=x+1;i<n;i++)
				result[i]=result[x];
		}
			if(result[x]==0) {
				for(int i=0;i<n;i++) {
					if(result[i]==1)
						counter++;
				}
				dif=b-counter;
			}
			else {
				for(int i=0;i<n;i++) {
					if(result[i]==0)
						counter++;
				}
				dif=a-counter;
			}
			for(int i=0;i<dif;i++)
				result[x+i]=result[x-1];
			for(int i=0;i<n;i++)
				System.out.print(result[i]);
			
		
	}
}//Wrong answer on test 7(I don,t know what the problem is with this code!!!)
