Bachet’s game is probably known to all but probably not
by this name. Initially there are
stones on the table. There are two
players Stan and Ollie, who move alternately. Stan always
starts. The legal moves consist in removing at least one but
not more than
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
numbers. Among the
numbers there is always
and thus the game never stalls.
Input
The input consists of a number of lines (between
and , inclusive). Each line describes
one game by a sequence of positive numbers. The first number is
the
number of stones on the table; the second number is
giving the
number of numbers that follow; the last 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 1 |
Sample Output 1 |
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
|
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins
|