CF1352F.Binary String Reconstruction

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.

对于某个二进制字符串 $s$（即每个字符 $s_i$ 要么是 '0'，要么是 '1'），我们写出其所有相邻（连续）字符对。换言之，我们写出所有长度为 $2$ 的子串。对每个这样的字符对（即长度为 $2$ 的子串），计算其中 '1'（数字 1）的个数。

你将获得三个整数：

• $n_0$ —— 所有连续字符对（子串）中，含 1 的个数等于 $0$ 的对的数量；
• $n_1$ —— 所有连续字符对（子串）中，含 1 的个数等于 $1$ 的对的数量；
• $n_2$ —— 所有连续字符对（子串）中，含 1 的个数等于 $2$ 的对的数量。

例如，对于字符串 $s =$ "1110011110"，写出的子串依次为："11"、"11"、"10"、"00"、"01"、"11"、"11"、"11"、"10"。因此，$n_0 = 1$，$n_1 = 3$，$n_2 = 5$。

你的任务是根据给定的 $n_0, n_1, n_2$ 恢复出任意一个满足条件的二进制字符串 $s$。题目保证 $n_0, n_1, n_2$ 中至少有一个大于 $0$，且解一定存在。

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 $n_0, n_1, n_2$ ($0 \le n_0, n_1, n_2 \le 100$; $n_0 + n_1 + n_2 \gt 0$). It is guaranteed that the answer for given $n_0, n_1, n_2$ exists.

第一行包含一个整数 $t$（$1 \le t \le 1000$）—— 表示输入中测试用例的数量。随后是各测试用例。

每个测试用例由一行组成，该行包含三个整数 $n_0, n_1, n_2$（$0 \le n_0, n_1, n_2 \le 100$；且 $n_0 + n_1 + n_2 \gt 0$）。保证对于给定的 $n_0, n_1, n_2$，答案一定存在。

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.

输出 $t$ 行。每行应包含一个对应于测试用例的二进制字符串。如果存在多种可能的解，输出任意一种即可。