Looking to combine a PC, Laptop and 2 monitors using a single keyboard and mouse

I have an HP Pavilion laptop for work, Two 2k monitors, a Gaming desktop, keyboard and mouse on a single desk. I'm looking to connect 2 monitors to the PC for gaming and also use both for dual screens for my laptop (want to keep laptop closed while working to minimize space) I'd like to connect both monitors via DP to the desktop and using HDMI to the laptop, again sharing the keyboard and mouse. There is no thunderbolt connection on the laptop unfortunately. What would be the best means to combine this environment? Do I need some sort of universal docking station perhaps?

Question by Scivic on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.