Runaway-A villain Deku story

This was once a story about Deku's sister but I decided to scrap that and turn it into a villain Deku story that focuses on Katsuki. In a lot of these we only really find out what it was like for him once he and Izuku meet up again.
I have decided to move the Sludge incident to earlier in their lives for maximum angst. I really am going to hate myself writing this and I apologise in advance if the writing is somehow good enough to make you upset.
SO DekDek runs away after the sludge incident and I don't know the rest.

Cover art by Kuro-Akumako on Deviantart.