Which one of the following alcohols reacts instantaneously with Lucas reagent?

The products $$\mathrm{A}$$ and $$\mathrm{B}$$ obtained in the following reactions, respectively, are

$$\begin{aligned} & 3 \mathrm{ROH}+\mathrm{PCl}_3 \rightarrow 3 \mathrm{RCl}+\mathrm{A} \\ & \mathrm{ROH}+\mathrm{PCl}_5 \rightarrow \mathrm{RCl}+\mathrm{HCl}+\mathrm{B} \end{aligned}$$

Major products A and B formed in the following reaction sequence, are

Consider the following reaction and identify the product (P).