1352F · Binary String Reconstruction

Problem: For some binary string $s$ (i.e. each character $s_i$ is either '0' or '1'), all pairs of consecutive (adjacent) characters were written. In other words, all substrings of length $2$ were written. For each pair (substring of length $2$), the number of '1' (ones) in it was calculated.

You are given three numbers:

• $n_0$ — the number of such pairs of consecutive characters (substrings) where the number of ones equals $0$;
• $n_1$ — the number of such pairs of consecutive characters (substrings) where the number of ones equals $1$;
• $n_2$ — the number of such pairs of consecutive characters (substrings) where the number of ones equals $2$.

For example, for the string $s=$"1110011110", the following substrings would be written: "11", "11", "10", "00", "01", "11", "11", "11", "10". Thus, $n_0=1$, $n_1=3$, $n_2=5$.

Your task is to restore any suitable binary string $s$ from the given values $n_0, n_1, n_2$. It is guaranteed that at least one of the numbers $n_0, n_1, n_2$ is greater than $0$. Also, it is guaranteed that a solution exists.

Input Format: The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases in the input. Then test cases follow.

Each test case consists of one line which contains three integers $n_0, n_1, n_2$ ($0 \le n_0, n_1, n_2 \le 100$; $n_0 + n_1 + n_2 > 0$). It is guaranteed that the answer for given $n_0, n_1, n_2$ exists.

Output Format: Print $t$ lines. Each of the lines should contain a binary string corresponding to a test case. If there are several possible solutions, print any of them.