Teaching my puppy to play nice with my cats

So I've just brought home a puppy this week (Harvey), he's a mix of boston terrier and not sure what the father was. He's a month and 2 weeks old. I have 3 indoor cats already, ones 3 years old (Spectre), but the other 2 are only 4 months old (Hannah and Felix). Now the older cat doesn't mind the dog at all, she's lived with dogs before and she just ignores him (already has shown him who was boss on first day), but this is all new for my kittens and they're very curious and of course playful. Now whenever the kittens play together, the puppy gets excited and tries to join in. The kittens have even already started to invite him to play by swatting at him gently and running around together. Harvey has been good so far and goes to bite and claw playfully, being careful not to make contact. But I've played with Harvey and his claws are sharp and when he's really excited, he has a strong bite. As the days pass, he seems to be getting more comfortable with playing with the kittens (and its only been 3 days), and I've noticed he doesn't hesitate as much when jumping on them.

Anyway, to the point, I know the kittens have safe places to run and are faster than the puppy, but of course I am very worried if he doesn't learn how to play nice with them very quickly, it could turn into a big problem when he gets older or lead to my kittens getting hurt. I'm just wondering if anyone has any advice or experience with this sort of thing. I want them to play nicely together and be friends.

Thank you for reading =)