Towers of Coins

Asen and Boyan play the following game. They fix two distinct positive integers K and L and start with a single tower of N coins. Asen always moves first, then Boyan, then Asen again, then Boyan, and so on, alternating turns. On a turn, the player may remove 1, K, or L coins from the tower. The player who takes the last coin (or coins) wins.

After playing for a long time, Asen realized that in some cases he can always win no matter how Boyan plays, while in all other cases Boyan, playing carefully, can always win no matter how Asen plays. Before the game starts, Asen wants to know which case he is in. Write a program that predicts the result of the game for the given K, L, and N.

The input describes m games.

The first line contains the integers K, L, and m with 1 < K < L < 10 and 3 < m < 50. The second line contains m integers N1, N2, …, Nm, where Ni is the number of coins in the i-th tower (1 ≤ Ni ≤ 1 000 000, i = 1, 2, …, m).

Print a single string of length m consisting of the letters A and B. If Asen wins the i-th game (no matter how the opponent plays), the i-th character must be A. If Boyan wins the i-th game (no matter how Asen plays), the i-th character must be B.