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replacing Na's in a vector with the preceding integer element

Hi,
I have a vector where an integer is followed by a randomly varying number of NA elements. I want to replace the NA's with the preceding integer. Let me explain with a simple?example :
avec<- c(1,NA,NA,5,NA,3,4,NA,NA,NA,NA,9,NA,0,NA,NA)
I want to get the following vector from a :
bvec<-c(1,1,1,5,5,3,4,4,4,4,4,9,9,0,0,0)

How can I do this with R? Will appreciate all the help that I can get.
Thanking you,
Ravi