OMCPLP 2013 Problem 3

An event occurs many years ago. It occurs periodically in $x$ consecutive years, then there is a break of $y$ consecutive years. We know that the event occured in $1964$ , $1986$ , $1996$ , $2008$ and it didn't occur in $1976$ , $1993$ , $2006$ , $2013$ . What is the first year in that the event will occur again?