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 B {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		int x = sc.nextInt();
		char ch = '0';
		if(a>b)
			ch = '0';
		else
			ch = '1';
		String s = "";
		for(int i=0;i<=x;i++){
			if(ch=='1')
				b--;
			else
				a--;
			s=s+ch;
			if(ch=='1')
				ch='0';
			else
				ch='1';
		}
		char tch = s.charAt(0);
		char tch2 = s.charAt(1);
		String remtch = "";
		String remtch2 = "";
		int count=0,count2=0;
		if(tch=='0'){
			count = a;
			count2=b;
		}
		else{
			count = b;
			count2=a;
		}
		while(count>0){
			remtch=remtch+tch;
			count--;
		}
		while(count2>0){
			remtch2=remtch2+tch2;
			count2--;
		}
//		System.out.println(s+" ");
		String stemp = s.substring(1,s.length());
		//System.out.println(stemp);
		
		String ans="";
		ans = ans + remtch+tch+remtch2+stemp;
		System.out.println(ans);
	}

}
