Cheryl's birthday

Albert and Bernard just met Cheryl and want to know her birthday. Cheryl gives ten possible dates:

May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17

She tells Albert the month and Bernard the day (privately). They then say:

• Albert: I don't know Cheryl's birthday, but I know that Bernard doesn't know either.
• Bernard: At first I didn't know Cheryl's birthday, but now I do.
• Albert: Then I know Cheryl's birthday too.

Assume perfect logical reasoning. What is Cheryl's birthday?