You can see how this is solved on RosettaCode by using (0+$n)->bnok($k) with the bigint pragma. In your case you might want Math::BigInt->new($y)->bnok($x) which will make sure the first argument is a proper object.
Shameless plug: if you find performance is an issue, use ntheory and its binomial function. It is faster for small integers, and also for large values if you have GMP on your system. It will return results as Math::BigInt if they're large. Worst case it falls back to Math::BigInt's bnok if the result is >64-bit and you don't have the GMP library.