## Coprime Nim

### Problem 560

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(10^{3}, 10^{3}) mod 1 000 000 007 = 954021836.

Find L(10^{7}, 10^{7}) mod 1 000 000 007