Here is the link:

http://www.unitedoffers.com/el/DMP?o...in.2004fly3.el

It does not include K.

Then click on the term and conditions and the answer is:

Qualifying Booking Classes: Qualifying travel may be booked in any booking class in United First, United Business or United Economy Class with a minimum roundtrip fare purchase of $250 or more. The fare purchased must be a valid, published fare. This promotion is not valid on government fares.

Which would include K assuming its a published fare? I would assume the terms and conditions would override anything else, but what I think and what UA thinks might not be the same.