Simulation Based Proof: How the Corrupted Party's Input is Given To Simulator
The simulator obtains "client $B$'s input" in the same way the simulator obtains $\:\{\hspace{-0.03 in}0,\hspace{-0.04 in}0\hspace{-0.03 in}\}\;$.

Even in the real world, the server computes its response without using any secrets, that response is the only message $B$ receives, and (from your description) no other party gives any output. $\:$ Thus, it doesn't matter what input the simulator sends to the trusted third party.