Does anybody know of a small keyboard with loop?

idk anything about instruments bc I am a classical pianist/cellist so I need a little help !

I gotta do some keyboard live looping (among normal old keyboarding) for a gig around February. I'm looking for a portable budget keyboard (2-3 octaves is good!) with loop&overdub for live looping. quantizing & being able to set the bpm, time signature, and # of meters for the loop is preferable (but not necessary). I would need 4 overdubs. I'm trying to keep the purchase under $50.

If you know of one I can buy, or a setup that would have the same effect, that would be sick :))