In what concerns the continuous evaluation solving exercises grade during the semester, you should submit until 23:59 of November 2nd
(this exercise will still be available for submission after that deadline, but without couting towards your grade)
[to understand the context of this problem, you should read the class #04 exercise sheet]

[AED017] Chocolate Boxes

John has N chocolate boxes available, each one with a certain amount of chocolates C_i. He wants to give one chocolate box to each of his friends, but since he wants to be as fair as possible he wants to choose which boxes to give in a way such that it minimizes the difference between the lowest and the highest number of chocolates a friend receives.

Can you help John discover how to do this and what is the smallest possible difference?

The Problem

Given a set of N chocolate boxes, the amount of chocolates C_i on each one and a number K of friends, your task is to compute the smallest possible difference between the lowest and the highest number of chocolates a friend receives if John gives exactly one box of chocolate to each of his K friends.

Input

The first input line contains two integers N (the amount of chocolate boxes) and K (the amount of friends).

The second line contains N space separated integers indicating the amount of chocolates in each box.

Output

The output should be a single line containing the smallest possible difference as previously described.

Constraints

The following limits are guaranteed in all the test cases that will be given to your program:

8 5
7 5 1 4 4 6 5 9

2

John could give the following boxes: {4,4,5,5,6} (with a difference of 6-4 = 2)