Is it true that if $bk\in Z(B\rtimes K)$ then $b\in Z(B)$?

Question

Is this fact true?

Let be $G= B \rtimes K$ and I suppose that $w=bk \in Z(G)$, with $b\in B$ and $k \in K$.

Is it then true that $b\in Z(B)$?

I have tried to prove it but I didn't succeed. Thanks!