I haven't been able to solve this problem for a long time (10 months), so I would greatly appreciate anyone can solve it or can provide hints.
For $$$ N, K \le 2*10^3 $$$ subtask we can use a straightforward DP, but I have no idea for DP optimization or Greedy algorithm for $$$ N, K \le 2*10^5 $$$ full task.
Examples:
6 2
2 -1 3 -4 -2 6
Answer: segments [1, 3] and [6, 6] with sum 10. No need to output which segments are used, just the sum itself.
This is the canonical problem for aliens trick (well, aside from IOI aliens): here's one of the first articles on it, as far as I can tell, and here are two more: two, three
Thanks, man, I didn't quite understand them but I will read them everyday and look for the day when I finally get it
:,). Also, NOI 2019 turns out to be exactly the same problem.