Basic idea of what scarlet letter is about?

It's about a young woman in a Puritan colony of America who has an affair (her husband went missing years earlier) with a priest in the colony. She is found out because she has a baby and has to wear a red "A" on her clothes to show her crime, but he priest is plagued with guilt his whole life. Basically the husband shows up and torments the priest until the priest dies of guilt.