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.Scanner;

public class Main {
	
	public static void main(String[] args) {
		
		Scanner scan = new Scanner(System.in);
	
		int a , b , x;
		a = scan.nextInt();
		b = scan.nextInt();
		x = scan.nextInt();
		
		String ans1 = try1(a , b , x);
		String ans2 = try2(a , b , x);
		if (ans1.isEmpty() == false) {
			System.out.println(ans1);
		} else {
			System.out.println(ans2);
		}
		
	}
	
	private static String try1(int a , int b , int x) {
		
		if (a == 0) {
			return "";
		}
		
		StringBuilder builder = new StringBuilder();
		builder.append("0");
		a --;
		int total = a + b;
		for (int i = 1;i <= total;i ++) {
			int prevValue = builder.charAt(i - 1) - '0';
			if (x == 1) {
				if (prevValue == 1) {
					if (a > 0) {					
						for (int j = 0;j < b;j ++) {
							builder.append("1");
						}
						for (int j = 0;j < a;j ++) {
							builder.append("0");
						}
						break;
					} else {
						return "";
					}
				} else {
					if (b > 0) {
						for (int j = 0;j < a;j ++) {
							builder.append("0");
						}
						for (int j = 0;j < b;j ++) {
							builder.append("1");
						}
						break;
					} else {
						return "";
					}
				}
			} else {
				if (prevValue == 1) {
					if (a > 0) {
						builder.append("0");
						a --;
						x --;						
					} else {
						return "";
					}
				} else {
					if (b > 0) {
						builder.append("1");
						b --;
						x --;
					} else {
						return "";
					}
				}
			}
		}
		return builder.toString();
		
	}
	
	private static String try2(int a , int b , int x) {
		
		if (b == 0) {
			return "";
		}
		StringBuilder builder = new StringBuilder();
		builder.append("1");
		b --;
		int total = a + b;
		for (int i = 1;i <= total;i ++) {
			int prevValue = builder.charAt(i - 1) - '0';
			if (x == 1) {
				if (prevValue == 1) {
					if (a > 0) {					
						for (int j = 0;j < b;j ++) {
							builder.append("1");
						}
						for (int j = 0;j < a;j ++) {
							builder.append("0");
						}
						break;
					} else {
						return "";
					}
				} else {
					if (b > 0) {
						for (int j = 0;j < a;j ++) {
							builder.append("0");
						}
						for (int j = 0;j < b;j ++) {
							builder.append("1");
						}
						break;
					} else {
						return "";
					}
				}
			} else {
				if (prevValue == 1) {
					if (a > 0) {
						builder.append("0");
						a --;
						x --;						
					} else {
						return "";
					}
				} else {
					if (b > 0) {
						builder.append("1");
						b --;
						x --;
					} else {
						return "";
					}
				}
			}
		}
		return builder.toString();
		
		
	}
	
    
}














