Anastasia and Barnabas play a game that starts with $330$ pebbles in a bowl. The game consists of two phases. The first phase looks as follows:
- First Anastasia announces an integer $A$ with $2\le A\le9$.
- Then Barnabas announces an integer $B$ with $2\le B\le9$ and $B\ne A$.
The second phase looks as follows:
- The two players alternately take pebbles out of the bowl. Anastasia makes the first move.
- In every move, Anastasia may either take $1$ pebble or $A$ pebbles.
- In every move, Barnabas may either take $1$ pebble or $B$ pebbles.
- The player who takes the last pebble wins the game.
Question: Which player is going to win this game? (As usual, we assume that Anastasia and Barnabas both use optimal strategies.)