K class is an "ultra-low" fare class on UA that they use for international. That's a mistake by SAS. I have seen K class IAD-NRT for $800 including tax.

The "ultra-low" fare classes, where significantly we cannot use our UA SWUs for international, are S, T, L and K. (I don't think they use L or T for international.)

I sometimes like to take the non-stop IAD-CPH when I go to Scandinavia but normally prefer to take the ARN-FRA-IAD on the way back, which departs ARN at 1 pm.

If I want to book Economy Extra for the CPH leg then I need to book with SAS even though UA will offer a ticket at the same exact price. Also, when I return on UA in Y or B class ticket (purchased from SAS) then I get the +50% EQM bonus on the UA transatlantic, which is nice. I can also upgrade the UA Y/B class flight with only 10,000 miles. I have never booked an S class ticket from SAS; I am sure that it could screw things up, i.e. no EQM bonus and maybe not even eligible for using a SWU to upgrade to business on UA.