Kai owns an apartment building held for investment purposes. The apartment building is worth $$500,000,$ although it is subject to a mortgage of $$100,000.$ Kai's basis in the apartment building is $$380,000.$ Kai exchanges the apartment building for an office building. The office building has an FMV of $$350,000.$ Kai receives $$50,000$ cash in addition to receiving the office building, and the other party assumes the apartment building mortgage. What is Kai's recognized gain on this exchange?

A$)$ $$0$

B$)$ $$50,000$

C$)$ $$120,000$

D$)$ $$150,000$