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. 
// CodeForces Round #1003 B competition

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class BinaryStringConstructing {

	int a,b,x;
	String so;

	private void readData(BufferedReader bin) throws IOException {
		String s = bin.readLine();
		String []ss = s.split(" ");
		a = Integer.parseInt(ss[0]);
		b = Integer.parseInt(ss[1]);
		x = Integer.parseInt(ss[2]);
	}

	void printRes() {
		System.out.println(so);
	}	
	
	String composeab(String st, int aa, int bb) {
		StringBuilder sb = new StringBuilder(st);
		for (int i=0; i<aa; i++) {
			sb.append("0");
		}
		for (int i=0; i<bb; i++) {
			sb.append("1");
		}
		return sb.toString();
	}
	String composeba(String st, int aa, int bb) {
		StringBuilder sb = new StringBuilder(st);
		for (int i=0; i<bb; i++) {
			sb.append("1");
		}
		for (int i=0; i<aa; i++) {
			sb.append("0");
		}
		return sb.toString();
	}

	private void calculate() {
		if (x==1) {
			so = composeab("", a, b);
			return;
		}
		int aa = a;
		int bb = b;
		if (bb >= aa) {
			String st = "0";
			aa--;
			while (x>1) {
				if (st.startsWith("0")) {
					st = "1" + st;
					bb--;
				} else {
					st = "0" + st;
					aa--;
				}
				x--;
			}
			so = composeab(st,aa,bb);			
		} else {
			String st = "1";
			bb--;
			while (x>1) {
				if (st.startsWith("0")) {
					st = "1" + st;
					bb--;
				} else {
					st = "0" + st;
					aa--;
				}
				x--;
			}
			so = composeba(st,aa,bb);
			
		}
	}

	public static void main(String[] args) throws IOException {
		// BufferedReader bin = new BufferedReader(new FileReader("cactus.in"));
		BufferedReader bin = new BufferedReader(
				new InputStreamReader(System.in));
		BinaryStringConstructing l = new BinaryStringConstructing();
		l.readData(bin);
		l.calculate();
		l.printRes();
	}
}
