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 Solution {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int numZero = sc.nextInt(), numOne = sc.nextInt();
		int x = sc.nextInt();
		int jx = x;
		StringBuilder sw = new StringBuilder();
		
		if(x%2==0) {
			if(numZero>numOne) {
				int val = 0;
				while(jx!=-1) {
					sw.append(val);
					if(val==0) {
						val=1;
						numZero--;
					}
					else {
						val=0;
						numOne--;
					}
					jx--;
				}
			}
			else {
				int val = 1;
				while(jx!=-1) {
					sw.append(val);
					if(val==0) {
						val=1;
						numZero--;
					}
					else {
						val=0;
						numOne--;
					}
					jx--;
				}
			}
		}
		else {
			int val = 1;
			while(jx!=-1) {
				sw.append(val);
				if(val==0) {
					val=1;
					numZero--;
				}
				else {
					val=0;
					numOne--;
				}
				jx--;
			}
		}
		
		int sl = sw.length();
		int flag=0,flaga=0;
		for(int i=0;i<sw.length();i++) {
			if(flag==1&&flaga==1)
				break;
			if(sw.charAt(i)=='0'&&flag==0) {
				while(numZero!=0)
					{sw.insert(i, 0);numZero--;}
				flag=1;
			}
			else if(sw.charAt(i)=='1'&&flaga==0) {
				while(numOne!=0)
					{sw.insert(i, 1);numOne--;}
				flaga=1;
			}
		}
		
		
		System.out.println(sw.toString());
		
	}
}