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Finesse or drop?

The following hand comes from a team competition where there's an element of point a board scoring:

North
5
K92
KQJ104
AQ63
South
QJ42
A8654
A
952
W
N
E
S
1
2
P
2
2
4
P
P
P

West leads A followed by a low spade.  You discard a club from dummy and East ruffs with 10.  You win the diamond return and cash A, East dropping Q.  You lead another heart and West plays low again.  Finesse or drop?  Why?

Finesse 9, hoping for an original QT with East.
Go up with K, hoping for an original QJT with East.
It's virtually a complete guess.

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