Let two ants stand on the perimeter of a regular 2019-gon of unit side length. One of them stands on a vertex and the other one is on the midpoint of the opposite side. They start walking along the perimeter at the same speed counterclockwise. The locus of their midpoints traces out a figure P in the plane with N corners. Let the area enclosed by convex hull of P be \frac{A}{B} \frac{\sin ^{m}\left(\frac{\pi}{4038}\right)}{\tan \left(\frac{\pi}{2019}\right)}, where A and B are coprime positive integers, and m is the smallest possible positive integer such that this formula holds. Find A+B+m+N.