Let $T(r)$ be the number of integer quadruplets $x, y, z, t$ such that $x^2 + y^2 + z^2 + t^2 \le r^2$. In other words, $T(r)$ is the number of lattice points in the four-dimensional hyperball of radius $r$.
You are given that $T(2) = 89$, $T(5) = 3121$, $T(100) = 493490641$ and $T(10^4) = 49348022079085897$.
Find $T(10^8) \bmod 1000000007$.
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