How many NAs do we have rowwise before the first numerical value in a dataframe?

I have this hypothetical dataframe

  df <- data.frame(K=c(NA, NA, 3, 4,0,2,NA, NA), A=c(NA, NA, NA, 4,0,3,NA, NA), B=c(NA, 2, NA, NA,0,NA,NA,0), C=c(0, 3, 5, NA,0,5,NA,5), D=c(NA, 3, 1, 2,0,10,NA,3))     df         K  A  B  C  D    1 NA NA NA  0 NA    2 NA NA  2  3  3    3  3 NA NA  5  1    4  4  4 NA NA  2    5  0  0  0  0  0    6  2  3 NA  5 10    7 NA NA NA NA NA    8 NA NA  0  5  3

I want to find rowwise how many NAs we have before the first numerical value (in that row) and I want to add this information as a last column in the above data frame

So I want to have

df2 <- data.frame(K=c(NA, NA, 3, 4,0,2,NA, NA), A=c(NA, NA, NA, 4,0,3,NA, NA), B=c(NA, 2, NA, NA,0,NA,NA,0), C=c(0, 3, 5, NA,0,5,NA,5), D=c(NA, 3, 1, 2,0,10,NA,3),        nn=c(3,2,0,0,0,0,5,2))    df2   K  A  B  C  D nn1 NA NA NA  0 NA  32 NA NA  2  3  3  23  3 NA NA  5  1  04  4  4 NA NA  2  05  0  0  0  0  0  06  2  3 NA  5 10  07 NA NA NA NA NA  10008 NA NA  0  5  3  2

For example, the first row contains 3 NAs before the first value of 0.The second row contains 2 NAs before the first value of 2.The third row contains zero NAs before the first value which is 3 and the same holds for the rows 4-6.For row seven we have only NAs,so in this case I just use the arbitrary value of 1000.For row eight we have two NAs before the first value of 0.

I tried this

DD<-apply(df,1,function(x) which(!is.na(x)))unlist(map(DD, 1) , use.names=FALSE)-1

but it does not work as I get

3 2 0 0 0 0 2

I miss the row that contains only NAs.Any ideas? Would it be possible to do that using dplyr?

Note that my real dataset contains 500 columns and 200000 rows. So a more general code would help a lot.