At a round table, 2015 people are sitting down, each of them is either a knight or a liar. Knights always tell the truth, liars always lie. They were given one card each, and on each card a number is written; all the numbers on the cards are different. Looking at the cards of their neighbours, each of those sitting at the table said: “My number is greater than that of each of my two neighbors.” After that, \(k\) of the sitting people said: “My number is less than that of each of my two neighbors.” At what maximum \(k\) could this occur?