So, my question is simple. Is there a Polish word "K", and what does it mean?
This is a very old preposition, once quite frequent in Polish, indicating the direction and associating itself with the dative case, which over time has been replaced in its basic function with the preposition "do" plus the genetive. It is still common in Russian and, I think, in Czech. "Ku" can be still heard in several fixed expressions like "ku mojemu zdziwieniu" or "ku przestrodze", "ku pamięci" [Ku pamięci, pamięci kupa, wpisał się Alojzy Dupa ]. It may be common when you want to describe a target which is either very distant [zwrócił wzrok ku słońcu] or rather undefined [świat zmierza ku zagładzie] or totally overhelming [podążam myślą ku przyszłości]. Or try to contemplate the following sentence to remember when "ku" is used: "Ku wściekłości prostytutek, Paryż myśli o legalizacji burdeli" - a headline from the Gazeta Wyborcza of the 26th of March 2010.