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.*;

public class problem1002B {
	public static void main(String[] args) {
		Scanner console = new Scanner(System.in);
		int num0 = console.nextInt();
		int num1 = console.nextInt();
		int diffConseq = console.nextInt();
		if (num1>num0) {
			String result = "10";
			num0--;
			num1--;
			diffConseq--;
			boolean add1 = true;
			while (diffConseq!=0) {
				diffConseq--;
				if (add1) {
					result+=1;
					num1--;
				}
				else {
					result+=0;
					num0--;
				}
				add1=!add1;
			}
			while (num1>0) {
				result=1+result;
				num1--;
			}
			if (result.charAt(result.length()-1) == '0') {
				while (num0>0) {
						result+=0;
						num0--;
				}
			} 
			else {
				result = result.substring(0, result.length()-1);
				while (num0>0) {
					result+=0;
					num0--;
				}
				result+=1;
			}
			System.out.println(result);
		}
		else {
			String result = "01";
			num0--;
			num1--;
			diffConseq--;
			boolean add1 = false;
			while (diffConseq!=0) {
			diffConseq--;
			if (add1) {
				result+=1;
				num1--;
			}
			else {
				result+=0;
				num0--;
			}
			add1=!add1;
		}
		while (num0>0) {
			result=0+result;
			num0--;
		}
		if (result.charAt(result.length()-1) == '1') {
			while (num1>0) {
					result+=1;
					num1--;
			}
		} 
		else {
			result = result.substring(0, result.length()-1);
			while (num1>0) {
				result+=1;
				num1--;
			}
			result+=0;
		}
		System.out.println(result);
		}
	}
}