The K station furthest east is Philadelphia's KYW-1060, which is still on air, and the W station furthest west was Fairbanks' WLAY, which operated in the early 1920s.
When the federal government began licensing commercial radio stations later that year, it had planned to assign call letters to the land-based stations in the same way. Somehow, things got flipped during implementation, though, and Eastern stations got W call signs and the Western ones got Ks. Where exactly does the Bureau of Navigation draw the line between East and West? For a while it ran north from the Texas-New Mexico border, but shifted in 1923 to follow the Mississippi River.
Yeah, the rules have never really been followed to a T. There are plenty of call sign anomalies. When the dividing line switched, some stations were made to change their call signs, while others weren't.