CF1003B Binary String Constructing

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 \le i < n $ ) such that $ s_i \ne 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 \le i < n $ and $ s_i \ne 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.

The first line of the input contains three integers $ a $ , $ b $ and $ x $ ( $ 1 \le a, b \le 100, 1 \le x < a + b) $ .

Print only one string $ s $ , where $ s $ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.

All possible answers for the first example: - 1100; - 0011. All possible answers for the second example: - 110100; - 101100; - 110010; - 100110; - 011001; - 001101; - 010011; - 001011.