I don't think its possible to solve C using 2D Segtree with lazy.

Let's think about the area covered by each pizza boy, can you see that it forms exactly a square, rotated 45 degrees?

So, the problem now is to find which points are covered by at least K squares. It can be done using Sweep Line. Rotate the squares, it'll become easier.

If you need more details, just talk to me. I still need to read problem B, I'll dedicate some time to it later.