The Meeting of the Minds

Buddha remembers his past lives, according to pretty much every every story. I don't know where there's a disagreement with that. He apparently had full memory of all his past incarnations. How? I don't mean, how did he remember it in the sense of, like, how can you do that? And was it such a powerful memory that he that there wasn't much of a distinction between the life he was in as the enlightened being and the previous lives?