Stick Game

Consider a game where two players remove sticks from a heap. The players move alternately, and the player who removes the last stick wins the game. A set P=\{p_1,p_2,\ldots,p_k\} determines the allowed moves. For example, if P=\{1,3,4\}, a player may remove 1, 3 or 4 sticks. Your task is find out for each number of sticks 1,2,\dots,n if the first player has a winning or losing position. Input