Let's call a lattice point $(x,y)$ inadmissible if $x,y$ and $x+y$ are all positive perfect squares.
For example, $(9,16)$ is inadmissible, while $(0,4)$, $(3,1)$ and $(9,4)$ are not.

Consider a path from point $(x_1,y_1)$ to point $(x_2,y_2)$ using only unit steps north or east.
Let's call such a path admissible if none of its intermediate points are inadmissible.

Let $P(n)$ be the number of admissible paths from $(0,0)$ to $(n,n)$.
It can be verified that $P(5)=252$, $P(16)=596994440$ and $P(1000)mod1000000007=341920854$.

Find $P(10000000)mod1000000007$.