# Problem 560: Coprime Nim
Coprime Nim is just like ordinary normal play Nim, but the players may
only remove a number of stones from a pile that is coprime with the
current size of the pile. Two players remove stones in turn. The player
who removes the last stone wins. Let L(n, k) be the number of losing
starting positions for the first player, assuming perfect play, when the
game is played with k piles, each having between 1 and n - 1 stones
inclusively. For example, L(5, 2) = 6 since the losing initial positions
are (1, 1), (2, 2), (2, 4), (3, 3), (4, 2) and (4, 4). You are also
given L(10, 5) = 9964, L(10, 10) = 472400303,
L(103, 103) mod 1 000 000 007 = 954021836. Find
L(107, 107) mod 1 000 000 007