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.io.PrintWriter;
import java.util.*;
import java.io.*;

public class codeforces2{
    static InputReader in = new InputReader();
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int ar[] = new int[2];
        ar[0] = in.nextInt();
        ar[1] = in.nextInt();
        int z = in.nextInt();
        StringBuilder sb = new StringBuilder();
        int s = 0;
        if(ar[0]<ar[1])
        s=1;
        String ret = "";
        int x = s;
        int y = s^1;
        if(z%2==0){
            while(z-->0){
                ret = ret+s;
                ar[s]--;
                s = s^1;
            }
            while(ar[x]-->1)
            ret = x+ret;
            while(ar[y]-->0)
            ret = ret+y;

            ret=ret+x;
        }
        else{
            //System.out.println("YES"+s+" "+z);
            z++;
            while(z-->0){
                ret = ret+s;
                //System.out.println(s+" "+ret);
                ar[s]--;
                s = s^1;
            }
            while(ar[x]-->0){
                ret = x+ret;
            }
            while(ar[y]-->0){
                ret = ret+y;
            }
        }

        out.println(ret);
        out.close();
    }
    static void debug(Object ...o){
        System.out.println(Arrays.deepToString(o));
    }
    static class InputReader{
        BufferedReader br;
        StringTokenizer st;
        
        public InputReader()
        {
            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;
        }
    }
}