Given an array of N integers, select K elements out of these N elements in such a way that the minimum difference between each of the K numbers is the largest. Your task is to print out the largest minimum difference after choosing any K elements.

Input

• The first line contains two integers N, K (1 ≤ N ≤ ~10^{5}~, 2 ≤ K ≤ N).

• The second line contains N integers.

All integers dont exceed ~10^{9}~.

Output

• The largest minimum difference after choosing K elements from N elements.

Sample Input

4 3

2 6 2 5

Sample Output

1

Sample Input

7 4

1 4 9 0 2 13 3

Sample Output

4