Statement

Luca's friend is tired of all new technological startup being created and, in response, wants to start a traditional business: a shopping mall. Before constructing the physical structure, she plans to carefully analyze the locations of already existing malls, as she obviously does not want to see her business cannibalized by competitors. On the path from Milan to Bergamo (near where Luca lives) there is an astonishing number of big malls, approximately aligned on a "virtual straight road". With the help of some acquaintances, she has obtained information about N malls. For each one, it is known the distance in kilometers from the center of Milan, considered at distance 0 by convention. The new mall must be constructed within this "virtual road" of lenght K, extremes included. Luca has been called to find the best position for his friend's new activity: where should he advise her to build the mall, in order to maximize the minimum distance with an existing mall?