The Game of 31

<p> The game of 31 was a favourite of con artists who rode the railroads in days of yore. The game<br /> is played with a deck of 24 cards: four labelled each of 1, 2, 3, 4, 5, 6. The cards in the deck are<br /> visible to both players, who alternately withdraw one card from the deck and place it on a pile.<br /> The object of the game is to be the last player to lay a card such that the sum of the cards in<br /> the pile does not exceed 31. Your task is to determine the eventual winner of a partially played<br /> game, assuming each player plays the remainder of the game using a perfect strategy.<br /> For example, in the following game player B wins: </p> <p> <img width="218" height="169" src="http://tk.hustoj.com/upload/pimg1342_1.png" alt="" /> </p>

<p> The input will consist of several lines; each line consists of a sequence of zero or more digits<br /> representing a partially completed game. The first digit is player A’s move; the second player<br /> B’s move; and so on. You are to complete the game using a perfect strategy for both players<br /> and to determine who wins. </p>

<p> For each game, print a line consisting of the input, followed by a space, followed by A or B to<br /> indicate the eventual winner of the game. </p>