export only last two fields?

here is my test file, with variable length of fields, each line is composed of letter only, and each line has at least 2 fields, fields were separated by dot (.)

abcd.abc.mlm
dft.dfasdf.bmk.kdjlka
ksdfalksdjfsl.tyu.ml
kasdjf.asdfkja.asdfj.asdf.df.m
lja.ml
aslkjdfjasldkf.sadlfkasdjlf.sdfasdfsa.asdfasdf.fdlm

I am trying to use sed to parse the test file, and only display the last two fields, like

abc.mlm
bmk.kdjlka
tyu.ml
df.m

At first my idea was something like ++ sed 's/!\.[a-z][a-z]*\.[a-z][a-z]*$/&/' test ++, and sure it did not work.

Any help? thank you!

fields.txt:

Really cool and thanks Glenn Arndt!


But still I have great interest in whether sed can do this

I think "pattern keeping method" should work, as following

sed 's/^.*\(\.[a-z][a-z]*\.[a-z][a-z]*$\)/\1/'

but apparently it does not. I am reading more sed help file trying to figure out why.

Thank you vgersh99!