Bachet’s Game

Bachet’s game is probably known to all but probably not by this name. Initially there are n stones on the ta- ble. There are two players Stan and Ollie, who move al- ternately. Stan always starts. The legal moves consist in re- moving at least one but not more than k stones from the table. The winner is the one to take the last stone. Here we consider a variation of this game. The number of stones that can be removed in a single move must be a member of a certain set of m numbers. Among the m numbers there is always 1 and thus the game never stalls. Input The input consists of a number of lines. Each line describes one game by a sequence of positive numbers. The first number is n ≤ 1000000 the number of stones on the table; the second number is m ≤ 10 giving the number of numbers that follow; the last m numbers on the line specify how many stones can be removed from the table in a single move. Output For each line of input, output one line saying either ‘Stan wins’ or ‘Ollie wins’ assuming that both of them play perfectly. Sample Input 20 3 1 3 8 21 3 1 3 8 22 3 1 3 8 23 3 1 3 8 1000000 10 1 23 38 11 7 5 4 8 3 13 999996 10 1 23 38 11 7 5 4 8 3 13 Sample Output Stan wins Stan wins Ollie wins Stan wins Stan wins Ollie wins