Can you get HIV through cannibalism?

This is purely theoretical. The question occurred after a long talk about zombies. If you were to ingest human meat (Hannibal Lecter style) and the human had HIV, could you contract the virus from the meat? Also, would it matter if you had cooked the meat or not? And would how long the meat sits out matter (HIV can't survive long out of a body)? Thank you. =)