Two players, Stan and Ollie, play, starting with two
natural numbers. Stan, the first player, subtracts any positive
multiple of the lesser of the two numbers from the greater of
the two numbers, provided that the resulting number must be
nonnegative. Then Ollie, the second player, does the same with
the two resulting numbers, then Stan, etc., alternately, until
one player is able to subtract a multiple of the lesser number
from the greater to reach 0, and thereby wins. For example, the
players may start with
$(25,7)$ and the game might progress
as
25 7
11 7
4 7
4 3
1 3
1 0
and Stan wins.
Input
The input consists of a number of lines. Each line contains
two positive integers less than $2^{31}$ giving the starting two
numbers of the game. Stan always starts. The last line of input
contains two zeroes and should not be processed.
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 |
34 12
15 24
0 0
|
Stan wins
Ollie wins
|