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 TestClass {
    public static void main(String args[] ) throws Exception {
        Scanner in=new Scanner(System.in);
        int a=in.nextInt();
        int b=in.nextInt();
        int x=in.nextInt();
        int c=0;
        if(a>b)c=1;
        for(int i=0;i<x;i++){
            if(c==0){
                System.out.print(1);
                b--;
                c=1;
            }else{
                System.out.print(0);
                a--;
                c=0;
            }
        }
        if(c==0){
            while(a>0){
                System.out.print(0);
                a--;
            }
            while(b>0){
                System.out.print(1);
                b--;
            }
        }
        else{
            while(b>0){
                System.out.print(1);
                b--;
            }
            while(a>0){
                System.out.print(0);
                a--;
            }
        }
    }
    static class Pair implements Comparable<Pair>{
        long x;
        int y;
        Pair(long a,int b){
            x=a;
            y=b;
        }
        public int compareTo(Pair o){
            if(x>o.x)return 1;
            else if(x==o.x)return o.y-y;
            else return -1;
        }
    }
    
}