Description

Today is Father's Day.Melo decided to play a little game to celebrate the important festival, meanwhile, Melo and Elliott are familar as father and son.

There are two piles of gold coins,one has $N$ and another has $M$ coins. Elliott and Melo take gold coins from two piles of gold coins in turn. (owing to the their relation, so Elliott take first)

Each person can take only one pile of any number of gold coins in one time.In the end, who has no gold coins to take,who gives all the gold coins to opponet after the game.

In order to win the game, both Elliott and Melo adopt the best strategy, please answer that Elliott and Melo who will win all the gold coins.How many gold coins did the winner get during the game?

Format

Input

The input contains multiple cases, each line contains two integers $N, M$ respectively, the number of coins per pile has.$(0\leq N,M \leq 10^5)$

Output

Print the name of the winner and the number of gold coins won by the winner during the game, separated by spaces, and each case of outputs is in one line.(If Elliott win, print “A”, or print “B”)

Samples

0 1
971 1

A 1
A 971

Hint