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 Solution {
    
     public static void main(String[] args) throws IOException {
         BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
         BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
         String[] parts = br.readLine().split(" ");
         int a = Integer.parseInt(parts[0]);
         int b = Integer.parseInt(parts[1]);
         int x = Integer.parseInt(parts[2]);
         int c0=0;
         int c1=0;
         int pairs=0;
         if(x%2!=0){
             c0=(x+1)/2;
             c1=c0;
             pairs = c1;
             c0 = a-c0;
             c1 = b-c1;
             if(c0>=0 && c1>=0){
                 while(c0>0){
                     bw.write("0");
                     c0--;
                 }
                 while(pairs>0){
                     bw.write("01");
                     pairs--;
                 }
                 while(c1>0){
                     bw.write("1");
                     c1--;
                 }
                 bw.newLine();
                 bw.flush();
                 bw.close();
                 br.close();
                 return;
             }
         }
         else{
             pairs = x/2;
             c0 = pairs;
             c1 = pairs;
             c0 = a-c0;
             c1 = b-c1;
             if(c1==0){
                 while(pairs>0){
                     bw.write("01");
                     pairs--;
                 }
                 while(c0>0){
                     bw.write("0");
                     c0--;
                 }
                 bw.newLine();
                 bw.flush();
                 bw.close();
                 br.close();
                 return;
             }
             else if(c0==0){
                 while(pairs>0){
                     bw.write("10");
                     pairs--;
                 }
                 while(c1>0){
                     bw.write("1");
                     c1--;
                 }
                 bw.newLine();
                 bw.flush();
                 bw.close();
                 br.close();
                 return;
             }
             else{
                 while(pairs>0){
                     bw.write("01");
                     pairs--;
                 }
                 while(c1>0){
                     bw.write("1");
                     c1--;
                 }
                 while(c0>0){
                     bw.write("0");
                     c0--;
                 }
                 bw.newLine();
                 bw.flush();
                 bw.close();
                 br.close();
                 return;
                 
             }
         }
     }
}