# Problem 576: Irrational jumps
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 \\dots\$, \$S(\\sqrt{\\frac 1 2}, 0.06,
0.3543)=1.4142 \\dots\$ and \$S(\\sqrt{\\frac 1 2}, 0.06,
0.2427)=16.2634 \\dots\$. 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 \\dots\$, since
\$S(\\sqrt{\\frac 1 2}, 0.06, 0.2427)+S(\\sqrt{\\frac 1 3}, 0.06,
0.2427)=29.5425 \\dots\$ is the maximal reachable sum for \$g=0.06\$.
\$M(10, 0.01)=266.9010 \\dots\$ Find \$M(100, 0.00002)\$, rounded to 4
decimal places.