1988C · Increasing Sequence with Fixed OR

Problem: 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.

Input Format: 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 $5\cdot 10^5$.

Output Format: 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.