Organizing of Rabbit Olympics is a difficult thing, even for such a dedicated rabbit as Stan. Stan tries to make the show spectacular, but also (being a patriot of his country) wants to make it easier for the audience to attend the grand event. Stan knows that the key to success - the simplification. So he simplified his country to one-dimension so that the location of each city in Rabbitland can be represented as one integer. Given the location of all cities. Stan can build no more than \textbf{K} stadiums. He is going to build them in the way to minimize the greatest distance (of course, one-dimensional), which the fans have to cover to the nearest stadium. Please help Stan to calculate this value. \InputFile The first line of input contains to space separated integers: the number of cities \textbf{N} (\textbf{1} ≤ \textbf{N} ≤ \textbf{100000}) and the number of stadiums \textbf{K} (\textbf{1} ≤ \textbf{K}≤ \textbf{100000}). The second line contains the list of city coordinates -- \textbf{N} space separated integers, which absolute value do not exceed \textbf{10^9}. \OutputFile Output the result with two digits after the decimal point in the single line.