Once upon a time, there was a kingdom ruled by a wise king.
After years of his reign, by means of successful economic actions, the kingdom, with n cities, became an economic power soon.
Without nation defense, the development of the state economy will be hurt, the king said.
After days of serious thoughts, the king finally decided to choose k cities to cover as more area as possible (the area covered by k cities equals to the area of the convex formed by these k points).
However, the king don't know how to choose the optimal way to do it. Please help him!