How to create a column that is a group label for unique collections of other columns data table

Question

Surprised how hard this is to find.

Suppose I have data table:

dat = data.table(d=c(1:3,1),k=c(3:1,3),f=1)

   d k f
1: 1 3 1
2: 2 2 1
3: 3 1 1
4: 1 3 1 

I want to groupby d,k to create a new column a that numbers the groups so I get:

   d k f a
1: 1 3 1 1
2: 2 2 1 2 
3: 3 1 1 3
4: 1 3 1 1

Please no workarounds, assume that d,k rows are not unique necessarily, so there might be repeats in a.