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.

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.

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.