P8284 "DAOI R1" Concert

> $ \texttt{I want to be an artist.} $

$ \texttt{Erinyes} $'s school is going to hold a concert, but if he wants to join it, he must pass an assessment first. The problem is as follows: Given two integers $ n,k $, meaning there are $ n $ students, you need to assign one number to each student, that is, for the integer $ n $, construct a sequence $ a $. The numbers given to the students must satisfy the following properties: - For each $ i\;(1 \leq i \leq n-1) $, it holds that $ a_i=\gcd(a_{i+1},a_{i+2},\dots,a_{n-1},a_n) $. - For each $ i\;(1 \leq i \leq n) $, it holds that $ 1 \leq a_i \leq 10^5 $. - For each $ i\;(1 \leq i \leq 10^5) $, $ a_i $ appears in the sequence at most $ k $ times. But this is too easy for $ \texttt{Erinyes} $, so he decides to focus on preparing for the performance, and leaves this problem to you. Your task is to output the number of such sequences $ l $ and all such sequences. Since the answer may be very large, the output rules are as follows: - If $ l=0 $, output ```Impossible```. - If $ 1 \leq l \leq 4 $, output the actual number of sequences, then output $ l $ lines, one sequence per line, representing the sequences you constructed. - If $ l \geq 5 $, output ```5 or more```, then output five lines, one sequence per line, representing the lexicographically smallest five among the sequences you constructed. - You must output in lexicographical order.

The first line reads an integer $ t $, meaning there are $ t $ test cases. For each test case, read two integers $ n,k $.

For each test case, output one integer or one string on the first line. If it is possible to construct, then output one sequence you constructed per line afterwards.

### Sample Explanation For the first test case, you can see that this solution is optimal. For the second test case, no matter what you do, it is impossible to construct a correct sequence. For the third test case, no matter what you do, it is impossible to construct a correct sequence. For the fourth test case, no matter what you do, it is impossible to construct a correct sequence. ### Constraints For $ 100\% $ of the testdata, $ 1 \leq t \leq 100,1 \leq n \leq 10^5,0 \leq k \leq 10^5 $. Translated by ChatGPT 5