PROBLEM IIT

You are given a rectangular grid defined by its bottom-left corner (x1, y1) and top-right corner (x2, y2).

You are also given a point (xc, yc) and a radius r.

Your task is to find all lattice points (x, y) such that:

1. The point lies inside or on the boundary of the rectangle.
2. The Euclidean distance from (x, y) to (xc, yc) is less than or equal to r.

INPUT

Seven integers: x1, y1, x2, y2, xc, yc, r

OUTPUT

Return a list of all lattice points (x, y) satisfying:

• x1 ≤ x ≤ x2
• y1 ≤ y ≤ y2
• (x - xc)^2 + (y - yc)^2 ≤ r^2

KEY INSIGHT

Instead of checking every point in the rectangle, iterate over: x in [xc - r, xc + r]

For each x, compute the valid range of y using: (y - yc)^2 ≤ r^2 - (x - xc)^2