Longest Increasing Subsequence with Reconstruction

Given an array of $n$ integers, find and return one **strictly** longest increasing subsequence (LIS). Your solution must run in $O(n \log n)$ time and $O(n)$ space. **Constraints:** - $0 \le n \le 10^5$ - Array elements can be any 32-bit integer (including negatives and duplicates) - "Strictly increasing" means no two equal elements are allowed in the subsequence - If multiple LIS exist with the same length, return any one of them **Example 1:** - Input: `[10, 9, 2, 5, 3, 7, 101, 18]` - Output: `[2, 3, 7, 18]` (length 4) - Explanation: `[2, 3, 7, 101]` is also valid. **Example 2:** - Input: `[0, 1, 0, 3, 2, 3]` - Output: `[0, 1, 2, 3]` (length 4) **Example 3:** - Input: `[7, 7, 7, 7]` - Output: `[7]` (length 1) - Explanation: Strictly increasing means equal elements cannot appear together.