Divisor game
Problem 550
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:
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.
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.
Give your answer modulo 987654321.