Adjudication query

I have an interesting situation in a game I'm GMing.  Powers and provinces may have been changed to protect the guilty.  I have no idea how to adjudicate this set of orders.

Italy:
A Serbia - Budapest
A Trieste S Serbia - Budapest

Russia:
A Vienna S Budapest - Trieste
A Budapest - Trieste

My first inclination is:

Italy:
A Serbia - Budapest
*A Trieste S Serbia - Budapest (Support goes through, dislodged by Budapest)

Russia:
A Vienna S Budapest - Trieste
A Budapest - Trieste

So Italy gains Budapest and Russia gains Trieste.

Am I right?

David Stewart