'01 W220. sometimes when the car is cold the starter will not crank when the key is turned. after a few tries it catches, engine cranks and fires right up.

I suspect a relay. I've searched around quite a bit and have read about the K40 relay. is this also the starter relay?? or is there a separate starter relay?? where are these relays located on an '01 W220?

besides the relay, is there anything else I should be looking at?

thanks!