Bachetâ€™s game is probably known to all but probably not
by this name. Initially there are
$n$ 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
$k$ 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
$n \leq 1000000$ the
number of stones on the table; the second number is
$m \leq 10$ 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 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
