Where does “cloakroom” come from?

I need to work through this etymology chain carefully. The chain provided is: - English room - Middle English rome - Middle Dutch clocke - Old Dutch klokka - Proto-Indo-European rowə- - Proto-Indo-European rewh₁- However, there's a problem: the headword is "cloakroom" but the chain appears to trace only "room" (and possibly "clock"). The chain doesn't actually explain "cloak" or how these elements combine into "cloakroom." Given the rules state "State only what the chain supports. Do not invent dates, cognates, or intermediate steps," I cannot write an accurate etymology for "cloakroom" based on this chain, as the chain is incomplete for the headword provided. If I'm meant to trace just the "room" component: Cloakroom derives from English room, which comes from Middle

cloakroom (English): A room intended for holding guests' cloaks and...