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The ball is live so if there is a contact foul it has to be a personal foul.
The definition of a free throw is that it is an unhindered try for goal.
Therefore, I would deem this to be an intentional personal foul and impose that penalty once the current FTs were finished -- much the same as is done when a player crosses the boundary plane and fouls the thrower.
If the current FT was made it counts due to continuous motion. If missed, I would have to strongly consider a substitute throw for disconcertion. Not sure if it meets the definition, but not convinced that it doesn't either.
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