A bouncing point moves counterclockwise along a circle with circumference $1$ with jumps of constant length $l<1$, until it hits a gap of length $g<1$, that is placed in a distance $d$ counterclockwise from the starting point. The gap does not include the starting point, that is $g+d<1$.

Let $S(l,g,d)$ be the sum of the length of all jumps, until the point falls into the gap. It can be shown that $S(l,g,d)$ is finite for any irrational jump size $l$, regardless of the values of $g$ and $d$.
Examples:
$S(\sqrt{\frac{1}{2}},0.06,0.7)=0.7071\cdots$, $S(\sqrt{\frac{1}{2}},0.06,0.3543)=1.4142\cdots$ and
$S(\sqrt{\frac{1}{2}},0.06,0.2427)=16.2634\cdots$.

Let $M(n,g)$ be the maximum of $\sum S(\sqrt{\frac{1}{p}},g,d)$ for all primes $p\le n$ and any valid value of $d$.
Examples:
$M(3,0.06)=29.5425\cdots$, since $S(\sqrt{\frac{1}{2}},0.06,0.2427)+S(\sqrt{\frac{1}{3}},0.06,0.2427)=29.5425\cdots$ is the maximal reachable sum for $g=0.06$.
$M(10,0.01)=266.9010\cdots$

Find $M(100,0.00002)$, rounded to $4$ decimal places.