R Cumean忽略Nas并用上一个有效值替换Na

类似于这个帖子Calculate cummean() and cumsd() while ignoring NA values and filling NAs，但我更愿意坚持tidyverse

我的数据:

structure(list(season = c("Winter", "Winter", "Winter", "Winter", 
"Winter", "Winter", "Winter", "Winter", "Winter", "Spring", "Spring", 
"Spring", "Spring", "Spring", "Spring", "Spring", "Spring", "Spring"
), tmean = c(NA, 2, 3, 4, NA, NA, NA, 8, NA, 7, 8, 9, NA, NA, 
5, 3, 2, NA)), class = "data.frame", row.names = c(NA, -18L))

season tmean
Winter    NA
Winter     2
Winter     3
Winter     4
Winter    NA
Winter    NA
Winter    NA
Winter     8
Winter    NA
Spring     7
Spring     8
Spring     9
Spring    NA
Spring    NA
Spring     5
Spring     3
Spring     2
Spring    NA

我想要的是:

season tmean cumtmean
Winter    NA       NA
Winter     2        2
Winter     3      2.5
Winter     4        3
Winter    NA        3
Winter    NA        3
Winter    NA        3
Winter     8     4.25
Winter    NA     4.25
Spring     7        7
Spring     8      7.5
Spring     9        8
Spring    NA        8
Spring    NA        8
Spring     5     7.25
Spring     3      6.4
Spring     2     5.66
Spring    NA     5.66