The theory of elliptic curves is involved with finding the number and properties of rational points -- that is, points whose x and y values are rational numbers -- and studying relationships between them. Elliptic curves, however, are curves of the form y^2 + ay + b = x^3 + cx^2 + dx + e. You feel that this type of equation is a bit too restrictive, and so you're going to generalize things a bit.
Given a String equation, and two ints xmax and ymax, find the number of lattice points (x,y) that satisfy equation and such that 0 <= x <= xmax and 0 <= y <= ymax. Lattice points are those with both coordinates being integers.
The string representing the equation follows the format "f(y)=g(x)", in more detail below:
Equation := Function(y) "=" Function(x)
(Function(x) is analogous to Function(y).)
If there are terms in a given function that are of the same power, consider their coefficients to be added together. For example, the equation "9y^3+5y^3=3+6" would be equivalent to "14y^3=9" (except that the latter is not in proper form and is thus illegal as input).
Note that no term of the form "Nx^0" will be allowed, to prevent ambiguity regarding 0^0.
|-||For C++ coders, the 64-bit integer type is long long (a gcc extension).|
|-||xmax will be between 0 and 1000000, inclusive|
|-||ymax will be between 0 and 1000000, inclusive|
|-||equation will be between 3 and 50 characters, inclusive|
|-||equation will follow the form "f(y)=g(x)" given above|
|-||no y between 0 and ymax, inclusive, will cause f(y) to exceed 2^63 - 1|
|-||no x between 0 and xmax, inclusive, will cause g(x) to exceed 2^63 - 1|
|-||no term of the form Nx^0 will be allowed in the input.|
|-||no term of the form Ny^0 will be allowed in the input.|