Binary String Constructing
Description
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.
Input
The first line of the input contains three integers $a$, $b$ and $x$ ($1 \le a, b \le 100, 1 \le x < a + b)$.
Output
Print only one string $s$, where $s$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Samples
2 2 1
1100
3 3 3
101100
5 3 6
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.