Valentine's Day
Valentine's Day is approaching, and Stepan, an enthusiastic fan of the holiday, has been given the task of selecting balloons to decorate the hall. At the university where Stepan studies, the student council president maintains a detailed inventory of all available balloons. There are N single-colored balloons, each with a diameter of D_i millimeters, where i ranges from 1 to N. According to the student council's new guidelines, at least K balloons must be used for the decoration. However, the student council president, who is not fond of Valentine's Day, has introduced a concept called the "ugliness index." This index is defined as the maximum possible difference D_i - D_j for 1 ≤ i, j ≤ M, where M is the number of balloons chosen for the hall, and D_i represents their diameters.
Your task is to assist Stepan in selecting M balloons (M ≥ K) from the N available balloons such that the ugliness index is minimized.
Input
The first line of the input contains two integers, N (2 ≤ N ≤ 100000) and K (2 ≤ K ≤ N). The second line contains N integers D_i (1 ≤ D_i ≤ 10^9), which represent the diameters of the balloons.
Output
The output should be the minimized ugliness index for the selected M balloons.