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 $L(10,5)=9964$, $L(10,10)=472400303$, $L({10}^3,{10}^3)mod1000000007=954021836$.

Find $L({10}^7,{10}^7)mod1000000007$.