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.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;
import java.util.StringTokenizer;
public class Main{
    
    public static void main(String[] args) throws IOException{
        // TODO Auto-generated method stub
    Reader.init(System.in);
    int a=Reader.nextInt();
    int b=Reader.nextInt();
    int x=Reader.nextInt();
    int temp=(x/2);
    int countera=0;
    int counterb=0;
    if(x%2==1) {
    if(a>b) {
        for(int i=0;i<a-temp;i++) {
            System.out.print(0);
            countera++;
        }
        for(int i=0;i<temp;i++) {
            if(counterb<b) {
            System.out.print(1);
            counterb++;
            }
            if(countera<a) {
            System.out.print(0);
            countera++;
            }
        }
        while(counterb<b) {
            System.out.print(1);
            counterb++;
        }
    }
    else{
        for(int i=0;i<b-temp;i++) {
            System.out.print(1);
            counterb++;
        }
        for(int i=0;i<temp;i++) {
            if(countera<a) {
            System.out.print(0);
            countera++;
            }
            if(counterb<b) {
            System.out.print(1);
            counterb++;
            }
        }
        while(countera<a) {
            System.out.print(0);
            countera++;
        }
    }
    }
    else {
        if(a>b) {
            for(int i=0;i<a-temp;i++) {
                System.out.print(0);
                countera++;
            }
            for(int i=0;i<b-temp+1;i++) {
                System.out.print(1);
                counterb++;
            }
            while(counterb<b) {
                System.out.print(0);
                System.out.print(1);
                countera++;
                counterb++;
            }
            System.out.print(0);
        }
        else {
            for(int i=0;i<b-temp;i++) {
                System.out.print(1);
                counterb++;
            }
            for(int i=0;i<a-temp+1;i++) {
                System.out.print(0);
                countera++;
            }
            while(countera<a) {
                System.out.print(1);
                System.out.print(0);
                countera++;
                counterb++;
            }
            System.out.print(1);
        }
    }

   }
}   
 
/** Class for buffered reading int and double values */
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
 
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
 
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
 
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
 