Binary String Constructing

题意翻译

### 题目描述 给你 $3$ 个整数 $a$ ,$b$ ,$x$ ，让你求出一个包含了 $a$ 个 $0$，$b$ 个 $1$ 的二进制串 $s$。要求其中 $s_i\not =s_{i+1}$ 的对数正好等于 $x$。 ### 输入格式 一行 $3$ 个整数 $a$ ,$b$ ,$x$。 ### 输出格式 一行一个字符串 $s$ ,表示**任意**一符合要求的答案。 ### 输入输出样例 无。 感谢 @win10 提供的翻译。

题目描述

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.

输入输出格式

输入格式

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

输出格式

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

输入输出样例

输入样例 #1

2 2 1

输出样例 #1

1100

输入样例 #2

3 3 3

输出样例 #2

101100

输入样例 #3

5 3 6

输出样例 #3

01010100

说明

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