Show HN: The parametric FizzBuzz problem is more interesting than the original

I recently ran across an interesting problem.

Every time I see FizzBuzz mentioned somewhere on the internet it is the same again and again and I was thinking:

That's a dumb problem like Russ Cox is saying.

But it gets interesting if it is a parametric FizzBuzz!

And what about unit testing it for all possible combinations of input?

How to achieve 100% coverage?