Which of the following would work best for the synthesis of the ether shown below?

Products $\left({\mathrm{P}}_2\right)\stackrel{\mathrm{anhydrous} \mathrm{HI}}{\leftarrow }({\mathrm{CH}}_3{)}_3\mathrm{C}-\mathrm{O}-{\mathrm{CH}}_3\stackrel{\mathrm{concentrated} \mathrm{HI}}{\to }$ Products $\left({\mathrm{P}}_1\right)$

The products ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are, respectively:

In the given reaction:

${\mathrm{CH}}_3-{\mathrm{CH}}_2-{\mathrm{CH}}_2-\mathrm{O}-{\mathrm{CH}}_2-{\mathrm{CH}}_2\stackrel{\mathrm{HCl}/∆}{\to }\left[\mathrm{X}\right]+\left[\mathrm{Y}\right]$, 

$\left[\mathrm{X}\right] \text{and} \left[\mathrm{Y}\right]$ will be, respectively:

The product $\mathrm{A}$ in the above reaction is:

The final product $\left(\mathrm{B}\right)$ is: