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.*;
import java.util.*;

public class Main{
    
    public static void main(String[] args) throws IOException {
        int a=in.nextInt();     // 0
        int b=in.nextInt();     // 1
        int x=in.nextInt();
        String S="10";
        a--;
        b--;
        x--;
        while(x>=2 && a>0 && b>0){
            S+="10";
            x-=2;
            a--;
            b--;
        }
        
        if(x==0){
            while(a>0){
                S=S+"0";
                a--;
            }
            while(b>0){
                S="1"+S;
                b--;
            }
        }
        else{
            if(a==0){
                while(b>0){
                    S=S+"1";
                    b--;
                }
            }
            else if(b==0){
                while(a>0){
                    S="0"+S;
                    a--;
                }
            }
            else{
                while(a>1){
                    S=S+"0";
                    a--;
                }
                while(b>0){
                    S="1"+S;
                    b--;
                }
                S="0"+S;
            }
        }
        println(S);
        in.close();
        out.close();
    }

    static int MIN = Integer.MIN_VALUE;
    static int MAX = Integer.MAX_VALUE;
    static Reader in = new Reader();
    static PrintWriter out = new PrintWriter(System.out);
    static void read(int arr[], int N) throws IOException{ for(int i=0;i<N;i++){ arr[i]=in.nextInt(); } }
    static void read(long arr[], int N) throws IOException{ for(int i=0;i<N;i++){ arr[i]=in.nextLong(); } }
    static void read(String arr[], int N) throws IOException{ for(int i=0;i<N;i++){ arr[i]=in.next(); } }
    static void print(Object O){ out.print(O); }
    static void println(Object O){ out.println(O); }
    static void print(int arr[]){ for(int i=0;i<arr.length;i++){ print(arr[i]+" "); } println(""); }
    static void print(int arr[][]){ for(int i=0;i<arr.length;i++){ print(arr[i]); } }
    static void debug(Object O){ System.out.println(O); }
}

class Reader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Reader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens() ) { tokenizer=new StringTokenizer(reader.readLine()); }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException { return Integer.parseInt(next()); }
    double nextDouble() throws IOException { return Double.parseDouble(next()); }
    long nextLong() throws IOException { return Long.parseLong(next()); }
    String nextLine() throws IOException { return reader.readLine(); }
    void close() throws IOException { reader.close(); }
}