Divisor game (noch nicht übersetzt)

Two players are playing a game, alternating turns. There are k piles of stones. On each turn, a player has to choose a pile and replace it with 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.