what size carb for 416?

[400exracer511]

What is the ideal size carb for a 416? I want to get a better one but it will probably have to be used due to a tight budget. Will a 450r carb work, if not, what size aftermarket is the best for motocross on a 416? Mods: k&n filter, white bros slip on, stage 2 hotcam, rev box (if that has any effect on carburation) and of course the 416 piston.

I want to get a full exhaust and port and polish in the future but i fear i will be wasting my money without a bigger carb.

thanks