# Problem 550: Divisor game

![graphic](img550.gif)

Two players are playing a game. There are k piles of stones. When it is
his turn a player has to choose a pile and replace it by two piles of
stones under the following two conditions: Both new piles must have a
number of stones more than one and less than the number of stones of the
original pile. The number of stones of each of the new piles must be a
divisor of the number of stones of the original pile. The first player
unable to make a valid move loses. Let f(n,k) be the number of winning
positions for the first player, assuming perfect play, when the game is
played with k piles each having between 2 and n stones
(inclusively).f(10,5)=40085. Find f(107,1012).Give your answer modulo
987654321.