D. Cute Sequencestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven 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.InputThe 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.OutputFor 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.ExampleInput
2
5 26 2
3 9 1
Output
4 5 6 13 26
-1
NoteConsider 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.
2
5 26 2
3 9 1

4 5 6 13 26 -1 
['binary search', 'brute force', 'greedy', 'math', '*2200']