在R中，如何将NA值替换为组的平均值？

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I have two data frames, the first (dat) has two columns group and value. The second data frame (dat2) has the mean value for each group. How would I replace the NA values in dat with the mean value of the group found in dat2?

library(dplyr)

x <- as.data.frame(seq(from = 1, to = 10, by = 1))
names(x)[1] <- "value"
y <- as.data.frame(c("A","A","A","A","A","B","B","B","B","B"),1)
names(y)[1] <- "group"

dat <- cbind(y,x)

dat[dat == 3] <- NA
dat[dat == 7] <- NA

dat2 <- dat %>%
  group_by(group) %>%
  summarise_at(.vars = names(.)[2],.funs = c(mean="mean"),na.rm=TRUE)