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Conditional mean for multiple columns in R?

My data is this:

train <- data.frame(y=c(1,2,1,1), x1=c(2,4,NA,5), x2=c(8,NA,6,12))

I need to replace for each x variable the missing values (NAs) with the mean of that column but the mean must be calculated using the values of that x variable that have a corresponding y value equal to the y value of the row of that missing value.

For instance: in the row where the NA of the x1 column is, the y value is equal to 1, so this missing value should be replaced with the mean between 2 and 5 (which are the x1 values for which y is also 1).

My code is like this but the mean is not conditional:

for(i in 1:ncol(train)){
  train[is.na(train[,i]), i] <- mean(train[,i], na.rm = TRUE)
}
library(dplyr)
train %>%
    group_by(y) %>%
    mutate_at(vars(-y), function(v){
        if_else(is.na(v), mean(v, na.rm = TRUE), v)
    }) %>%
    ungroup()
## A tibble: 4 x 3
#      y    x1    x2
#  <dbl> <dbl> <dbl>
#1     1   2       8
#2     2   4     NaN
#3     1   3.5     6
#4     1   5      12

We can use na.aggregate after grouping by the 'y' column

library(dplyr)
library(zoo)
train %>%
  group_by(y) %>%
   mutate_at(vars(-one_of(group_vars(.))),
             ~if(all(is.na(.))) NA_real_ else na.aggregate(.))
# A tibble: 4 x 3
# Groups:   y [2]
#      y    x1    x2
#  <dbl> <dbl> <dbl>
#1     1   2       8
#2     2   4      NA
#3     1   3.5     6
#4     1   5      12

Or apply na.aggregate after split ting the dataset into a list of data.frame s based on 'y' column

train[-1] <- unsplit(lapply(split(train[-1], train$y), na.aggregate), train$y)

Consider ave for groupwise mean wrapped inside an ifelse for NA condition or not:

# ITERATE THROUGH ALL COLUMNS BUT FIRST
for(i in c("x1", "x2")) {    
    train[[i]] <- ifelse(test = is.na(train[[i]]), 
                         yes = ave(train[[i]], train$y, FUN=function(x) mean(x, na.rm=TRUE)), 
                         no = train[[i]])
}

train   
#   y  x1  x2
# 1 1 2.0   8
# 2 2 4.0 NaN
# 3 1 3.5   6
# 4 1 5.0  12

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