You are given a 0-indexed integer array nums, where nums[i] represents the score of the ith student. You are also given an integer k.

Pick the scores of any k students from the array so that the difference between the highest and the lowest of the k scores is minimized.

Return the minimum possible difference. Hint: You can sort the array before using the Sliding window algorithm.

Input

The first line contains 2 integers n and k, which are the length of array nums and the window size, relatively.

The second line contains n integers which are the elements of array nums.

Output

Minimum possible difference

Example 1

Input

1 1
90

Output

0

Example 2

Input

4 2
9 4 1 7

Output

2