CF1166D Cute Sequences

Given a positive integer $ m $ , we say that a sequence $ x_1, x_2, \dots, x_n $ of positive integers is $ m $ -cute if for every index $ i $ such that $ 2 \le i \le n $ it holds that $ x_i = x_{i - 1} + x_{i - 2} + \dots + x_1 + r_i $ for some positive integer $ r_i $ satisfying $ 1 \le r_i \le m $ . You will be given $ q $ queries consisting of three positive integers $ a $ , $ b $ and $ m $ . For each query you must determine whether or not there exists an $ m $ -cute sequence whose first term is $ a $ and whose last term is $ b $ . If such a sequence exists, you must additionally find an example of it.

The first line contains an integer number $ q $ ( $ 1 \le q \le 10^3 $ ) — the number of queries. Each of the following $ q $ lines contains three integers $ a $ , $ b $ , and $ m $ ( $ 1 \le a, b, m \le 10^{14} $ , $ a \leq b $ ), describing a single query.

For each query, if no $ m $ -cute sequence whose first term is $ a $ and whose last term is $ b $ exists, print $ -1 $ . Otherwise print an integer $ k $ ( $ 1 \le k \leq 50 $ ), followed by $ k $ integers $ x_1, x_2, \dots, x_k $ ( $ 1 \le x_i \le 10^{14} $ ). These integers must satisfy $ x_1 = a $ , $ x_k = b $ , and that the sequence $ x_1, x_2, \dots, x_k $ is $ m $ -cute. It can be shown that under the problem constraints, for each query either no $ m $ -cute sequence exists, or there exists one with at most $ 50 $ terms. If there are multiple possible sequences, you may print any of them.

Consider the sample. In the first query, the sequence $ 5, 6, 13, 26 $ is valid since $ 6 = 5 + \bf{\color{blue} 1} $ , $ 13 = 6 + 5 + {\bf\color{blue} 2} $ and $ 26 = 13 + 6 + 5 + {\bf\color{blue} 2} $ have the bold values all between $ 1 $ and $ 2 $ , so the sequence is $ 2 $ -cute. Other valid sequences, such as $ 5, 7, 13, 26 $ are also accepted. In the second query, the only possible $ 1 $ -cute sequence starting at $ 3 $ is $ 3, 4, 8, 16, \dots $ , which does not contain $ 9 $ .