## Divisor game

### Problem 550

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(10^{7},10^{12}).

Give your answer modulo 987654321.