문제<\/h2>
Préférence<\/em> is a card game which is very popular in Eastern Europe. It is usually played with a 32-card deck, which consists of pip cards from 7 to 10, Jack, Queen, King, and Ace in each of the four suits: Spades, Clubs, Diamonds, and Hearts. In each round of the game, three players receive ten cards each, and two cards are left on the table as a talon. Then, a phase of auction happens, where players make their bids, which are obligations to take at least a certain number of tricks. A special case of a bid is a so-called misère<\/em>, which is an obligation to take no tricks regardless of other players' moves.<\/p>
In this task, we will consider a special modification of préférence which is played with a modified deck containing $A<\/mi>\cdot<\/mo>B<\/mi><\/mrow>A\cdot B<\/math><\/span><\/span> A<\/span> <\/span> \cdot<\/span> <\/span><\/span> <\/span> B<\/span><\/span><\/span><\/span> cards, where A<\/mi><\/mrow>A<\/math><\/span><\/span> A<\/span><\/span><\/span><\/span> is a number of suits, and B<\/mi><\/mrow>B<\/math><\/span><\/span> B<\/span><\/span><\/span><\/span> is the number of ranks in each suit. For example, the standard 32-card deck for the préférence game has A<\/mi>=<\/mo>4<\/mn><\/mrow>A = 4<\/math><\/span><\/span> A<\/span> <\/span> =<\/span> <\/span><\/span> <\/span> 4<\/span><\/span><\/span><\/span> suits and$

Misère