Given a circle of radius \sqrt{13}, let A be a point at a distance 4+\sqrt{13} from the center O of the circle. Let B be the point on the circle nearest to point A. A line passing through the point A intersects the circle at points K and L. The maximum possible area for \triangle B K L can be written in the form \frac{a-b \sqrt{c}}{d}, where a, b, c, and d are positive integers, a and d are relatively prime, and c is not divisible by the square of any prime. Find a+b+c+d.