I would say neither:
Input device examples include mouse, keyboard, camera, joystick ....
Output devices include printer, monitor, modem .....
The hard drive would be a storage device, a category which also includes memory (temporary storage) ...
Check the glossary of any reliable comptuer text. or search for a glossary on line, for clarification....
(some might say it is both, but that is a real stretch, in my view...one stores info to it, or retrieves info from it, but in a purist sense, it is neither input nor output.)