Conditionally replace elements of a vector based on an index

It's best explained with an example.

I have a vector, or column from data.frame named vec:

vec <- c(NA, NA, 1, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA)

I would like a vectorized process (not a for loop) to change the three trailing NA when a 1 is observed.

The end vector would be:

c(NA, NA, 1, 1, 1, 1, NA, 1, 1, 1, 1, NA, NA, NA)

If we had:

vec <- c(NA, NA, 1, NA, 1, NA, NA, 1, NA, NA, NA, NA, NA, NA)

The end vector would look like:

c(NA, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, NA, NA, NA)

A very badly written solution is:

vec2 <- vec
for(i in index(v)){
  if(!is.na(v[i])) vec2[i] <- 1
  if(i>3){
    if(!is.na(vec[i-1])) vec2[i] <- 1
    if(!is.na(vec[i-2])) vec2[i] <- 1
    if(!is.na(vec[i-3])) vec2[i] <- 1
  }
  if(i==3){
    if(!is.na(vec[i-1])) vec2[i] <- 1
    if(!is.na(vec[i-2])) vec2[i] <- 1
  }
  if(i==2){
    if(!is.na(vec[i-1])) vec2[i] <- 1
  }
}