https://mirror.codeforces.com/problemset/problem/1215/B

https://mirror.codeforces.com/contest/1215/submission/60611022

Here's a problem and Um_nik's solution to it.
I was thinking about a lot of things, tried DP etc. and was unable to solve it.
Then I saw this crazily concise solution of Um_nik.
Can someone explain, what's his approach?
Like, I understood what he's doing, but didn't understand why it's working, or I should rather say, how he came to this solution.
Like the idea, or some convincing observation behind this idea.