CF1988C Increasing Sequence with Fixed OR

You are given a positive integer $ n $ . Find the longest sequence of positive integers $ a=[a_1,a_2,\ldots,a_k] $ that satisfies the following conditions, and print the sequence: - $ a_i\le n $ for all $ 1\le i\le k $ . - $ a $ is strictly increasing. That is, $ a_i>a_{i-1} $ for all $ 2\le i\le k $ . - $ a_i\,|\,a_{i-1}=n $ for all $ 2\le i\le k $ , where $ | $ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 1000 $ ). Description of the test cases follows. The only line of each test case contains one integer $ n $ ( $ 1\le n\le 10^{18} $ ). It's guaranteed that the sum of lengths of the longest valid sequences does not exceed $ 5\cdot 10^5 $ .

For each testcase, print two lines. In the first line, print the length of your constructed sequence, $ k $ . In the second line, print $ k $ positive integers, denoting the sequence. If there are multiple longest sequences, you can print any of them.