# Problem 403: Lattice points enclosed by parabola and line
For integers a and b, we define D(a, b) as the domain enclosed by the
parabola y = x2 and the line y = a·x + b:D(a, b) = { (x, y) | x2 ≤ y ≤
a·x + b }. L(a, b) is defined as the number of lattice points contained
in D(a, b). For example, L(1, 2) = 8 and L(2, -1) = 1. We also define
S(N) as the sum of L(a, b) for all the pairs (a, b) such that the area
of D(a, b) is a rational number and |a|,|b| ≤ N. We can verify that S(5)
= 344 and S(100) = 26709528. Find S(1012). Give your answer mod 108.