{"app":{"locale":"en-GB"},"problem":{"content":"

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 $\\{1,2,3,5,8,13,\\ldots\\}$ 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.

$\"p662_fibonacciwalks.png\"$

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 $F(10\\,000,10\\,000) \\bmod 1\\,000\\,000\\,007$.

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