I am going in July as I'll be in Berlin for the whole month and will most likely take the SAS flights. Thought if you are looking to do it all on *A double check because some days/times the flights listed on SAS are actually operated by Icelandair.

As others have said there is also the LH flight.

If you aren't worried about miles then do as others have said and book with Icelandair and take advantage of their free stop over and do an add on to Europe.