BGP Default route conditional advertising

I have 2 routers (R1and R2) are in separate sites and both have internet connection (using default static route) and connected to the branches by BGP . I want to configure them to advertise default route to the branches and all the branches use R1 as primary as long as its internet connection is active . In brief I want to configure R1(the primary) to advertise Default route as long as it has active internet connection