Problem B: Euclid's Game
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):
25 7
11 7
4 7
4 3
1 3
1 0
an Stan wins.
The input consists of a number of lines. Each line contains two
positive integers giving the starting two numbers of the game.
Stan always starts.
For each line of input, output one line saying either Stan wins
or Ollie wins assuming that both of them play perfectly.
The last line of input contains two zeroes and should not be processed.
Sample input
34 12
15 24
0 0
Output for sample input
Stan wins
Ollie wins