Alice walks on a lattice grid. She can step from one lattice point $A(a,b)$ to another $B(a+x,b+y)$ providing distance $AB=\sqrt{x^2+y^2}$ is a Fibonacci number $\{1,2,3,5,8,13,\dots \}$ and $x\ge 0,$ $y\ge 0$.

In the lattice grid below Alice can step from the blue point to any of the red points.

Let $F(W,H)$ be the number of paths Alice can take from $(0,0)$ to $(W,H)$.
You are given $F(3,4)=278$ and $F(10,10)=215846462$.

Find $F(10000,10000)mod1000000007$.