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.*;
import java.io.*;

public class Main
{
	public static void main(String[] args)
	{
	    //test
		FastReader reader = new FastReader();
		PrintWriter writer = new PrintWriter(System.out);

		int a = reader.nextInt();
		int b = reader.nextInt();
		int x = reader.nextInt();

		int low=0, high=0;
		String l="", r="";

		if (a < b)
		{
			low = a;
			high = b;
			l = "0";
			r = "1";
		}
		else
		{
			low = b;
			high = a;
			l = "1";
			r = "0";
		}

		String ans = "";

		if (x%2 == 0)
		{
			for (int i=1; i<=x/2; i++)
			{
				ans = ans + r + l;
				low--;
				high--;
			}

			while (low > 0)
			{
				ans = ans + l;
				low--;
			}

			while (high > 0)
			{
				ans = ans + r;
				high--;
			}
		}
		else
		{
			for (int i=1; 2*i<=x; i++)
			{
				ans = ans + r + l;
				low--;
				high--;

			}

			while (high > 0)
			{
				ans = ans + r;
				high--;
			}

			while (low > 0)
			{
				ans = ans + l;
				low--;
			}
		}

		writer.println(ans);
		writer.close();
	}

	static class FastReader
	{
		BufferedReader br;
		StringTokenizer st;

		public FastReader()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next()
		{
			while (st == null || !st.hasMoreElements())
			{
				try
				{
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(next());
		}

		long nextLong()
		{
			return Long.parseLong(next());
		}

		double nextDouble()
		{
			return Double.parseDouble(next());
		}

		String nextLine()
		{
			String str = "";
			try
			{
				str = br.readLine();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}
			return str;
		}
	}
}