The Game of 31

The game of 31 was a favourite of con artists who rode the railroads in days of yore. The game is played with a deck of $24$ cards: four of each of 1, 2, 3, 4, 5, 6 (four cards labelled 1, four labelled 2, and so on). Initially all of the cards lie face up on the table and the discard pile is empty. The players then take turns. On each turn the current player picks up one unused card from the table and lays it on the discard pile. The goal is to be the last player to lay a card without letting the sum of the pile exceed $31$. Your task is to determine the eventual winner of a partially played game, assuming both players play the remainder of the game with a perfect strategy.

For example, in the following game player $B$ wins:

1. Player $A$ plays 3.
2. Player $B$ plays 5.
3. Player $A$ plays 6.
4. Player $B$ plays 6.
5. Player $A$ plays 5.
6. Player $B$ plays 6.

After player $B$'s final 6 the pile totals exactly $31$, so player $A$ can no longer move and player $B$ is the winner.

The first line contains the number of test cases. Each of the following lines describes one test case: a sequence of zero or more digits representing a partially completed game. The first digit is player $A$'s move, the second is player $B$'s move, and so on, with the two players alternating. Finish each game using a perfect strategy for both players to determine who wins.

For each game, print A or B on its own line to indicate the eventual winner.