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.*;
public class MyClass {
    public static void main(String args[]) 
    {
        Scanner sc=new Scanner(System.in);
        int a=sc.nextInt();
        int b=sc.nextInt();
        int x=sc.nextInt();
        int count[]=new int[2];
        count[0]=a;
        count[1]=b;
        String r="";
       int s=0;
        while(x>=0)
        {
            //System.out.println(r+" "+s+" "+count[s]);
           if(count[s]==0)
           {
               r=1+r;
               count[1]--;
              
           break;
           }
           else
           {
               r=r+s;
               count[s]--;
               if(s==0)
               s=1;
               else
               s=0;
               x--;
           }
        }
        String gen0=gen(0,count[0]);
        String gen1=gen(1,count[1]);
        int l=r.length();
        for(int i=0;i<l;i++)
        {
            if(r.charAt(i)=='0')
            {
                r=r.substring(0,i+1)+gen0+r.substring(i+1,l);
                break;
            }
        }
        l=r.length();
        for(int i=0;i<l;i++)
        {
            if(r.charAt(i)=='1')
            {
                r=r.substring(0,i+1)+gen1+r.substring(i+1,l);
                break;
            }
        }
        
        
        
        System.out.println(r);
        
        
    }
    public static String gen(int a,int c)
    {
        String res="";
        for(int i=1;i<=c;i++)
        res=res+a;
        return res;
    }
}
