Time travel with Memories

There’s a ff I’ve been trying to find to read again that involves Tom and Harry going back in time. They know they’re going back in time prior and while deciding different things about the new world they get drunk and end up changing a lot of things. I remember that one of them change the sorting hat into a tea kettle and it sorts people. Another one is Tom trying to save Neville’s parents but he’s not able to. I believe Tom ends up being the defense professor and Dumbledore hates it.