Two Kings and Their Estate

There are two kings George and Alex quarreling over a precious state of $N$ lands connected by $N-1$ roads. There are $a$i gold coins in the $i$th land. Both of them want to win such a precious state. In order to win this state, they decided to play a game as follows. There is a genie who knows the state very well and he is the one who can collect gold coins from any land of the state. But he can