408851: GYM103351 A Modulo Sequence
Memory Limit:256 MB
Time Limit:1 S
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Description
A. Modulo Sequencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output
You are given a single positive integer $$$M$$$. Construct an array of positive integers $$$a_1, \ldots, a_n$$$ such that:
- $$$1 \le a_i \le M$$$ for all $$$1 \le i \le n$$$;
- $$$a_i \bmod a_{i-1} = a_{i-2}$$$ for all $$$3 \le i \le n$$$;
- The size of the array $$$n$$$ is largest possible.
The first line of the input contains a single integer $$$T$$$ — the number of test cases ($$$1 \le T \le 10$$$).
Each test case is given as a line containing a single integer $$$M$$$ ($$$1 \le M \le 10^9$$$).
OutputOutput exactly two lines for each test case. The first line should contain a single integer $$$n$$$ — the size of your array.
The second line should contain $$$n$$$ space-separated integers $$$a_1, \ldots, a_n$$$ — the array itself.
ExampleInput2 2 3Output
3 1 2 1 4 1 2 3 2