Crossword Genius

Flat on the floor, one may welcome you (3)

Ross

I believe the answer is:

mat

I'm a little stuck... Click here to teach me more about this clue!

'flat' is the definition.
(I know that flat can be written as mat)

'on the floor one may welcome you' is the wordplay.
I cannot quite understand how this works, but
'on' could be 'at' (I've seen this in other clues) and 'at' is located in the answer.
A single letter 'm' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for mat that I've seen before include "Shoe-cleaner" , "Paint with a dull surface" , "Unglossy floor pad" , "Rough piece of floor-covering" , "Small carpet" .)

I've seen this clue in the Evening Standard.
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