== include(page="template/taskheader" task_id="fairgame") ==

Alice and Bob are playing a game. They have a pile of N rocks. Alice makes the first move, then Bob does the second, and so on... In each turn, the player that has to move takes at least 1 rock and maximum K rocks. If one takes an odd number of rocks, then they have to pay M dollars. When the pile is empty, the player who made the last move gets P dollars and the other one gets Q dollars. Knowing that they play optimally, which means Alice wants to maximize the difference in dollars between them and Bob wants to minimize this difference.

Alice and Bob are playing a game. They have a pile of N rocks. Alice makes the first move, then Bob does the second, and so on... In each turn, the player that has to move takes at least 1 rock and maximum K rocks. If one takes an odd number of rocks, then they have to pay M dollars. When the pile is empty, the player who made the last move gets P dollars and the other one gets Q dollars. After the game ends, Alice will end up with an amount of dollars, let's call it X, and Bob will end up with another amount of dollars, let's call it Y. Knowing that they play optimally, which means Alice wants to maximize the number X - Y Bob wants to minimize this number, then find out X - Y after the game ends.

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