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 practice2 {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int a = s.nextInt();
		int b = s.nextInt();
		int x = s.nextInt();
		String str = "";
		if(a>b) {
			str=str+0;
			a--;
		}
		else {
			str=str+1;
			b--;
		}
		System.out.println(binarystring(a, b, x, str, 0));
	}

	static String binarystring(int a, int b, int x, String output, int index) {
		if (a == 0 && b == 0)
			return output;
		char last = output.charAt(index);
		int num = last - '0';
		if (x == 1) {
			if (num == 0) {
				for (int i = 0; i < a; i++)
					output = output + 0;

				for (int i = 0; i < b; i++)
					output = output + 1;

			} else if (num == 1) {
				for (int i = 0; i < b; i++)
					output = output + 1;

				for (int i = 0; i < a; i++)
					output = output + 0;
			}
			a = 0;
			b = 0;
		} else if (x > 1) {
			if (num == 0) {
				if (b != 0) {
					output = output + 1;
					b--;
				}
			} else {
				if (a != 0) {
					output = output + 0;
					a--;
				}
			}
			index++;
		}
		String ans = binarystring(a, b, x - 1, output, index);
		return ans;

	}
}
