Should I wish my ex a happy birthday?

Me and my ex went no contact months ago, won’t get into detail why we did cus it’s a long story but last we on instagram I got a notification from him that he deleted our shared album and ngl I was laughing cus it was so cringe 😭 but I responded with something funny and we just had a small lil talk (I made sure NOT to make it long cus I know myself too well) and we were honestly cool. This week his birthday is coming up and should I say happy birthday to him? I expect nothing in return and I honestly don’t really want to start anything with him, I just genuinely want to wish him a happy birthday & a happy day :) I really don’t care if he doesn’t wish me a happy birthday back because that’s not the reason why I’m wishing him