A network engineer is tasked with designing a network for a new office building. The building will have $5$ different floors, with each floor requiring its own subnet. The IP range allocated for the building is $10\mathrm{.}0\mathrm{.}0\mathrm{.}0/22.$ The engineer wants to ensure that each floor can support up to $200$ devices.

What is the minimum subnet mask the engineer can use for each floor's subnet to meet this requirement?

$255\mathrm{.}255\mathrm{.}255\mathrm{.}0$

$255\mathrm{.}255\mathrm{.}252\mathrm{.}0$

$255\mathrm{.}255\mathrm{.}254\mathrm{.}0$

$255\mathrm{.}255\mathrm{.}255\mathrm{.}128$