A11957 | 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.