IMO Shortlist 2013 problem C2

  Avg: 0,0
  Avg: 6,0
Dodao/la: arhiva
21. rujna 2014.
In the plane, 2013 red points and 2014 blue points are marked so that no three of the marked points are collinear. One needs to draw k lines not passing through the marked points and dividing the plane into several regions. The goal is to do it in such a way that no region contains points of both colors.

Find the minimal value of k such that the goal is attainable for every possible configuration of 4027 points.
Izvor: Australia