Mirko's newest math homework assignment is a very difficult one! Given a sequence, ~V~, of ~N~ integers, remove exactly ~K~ of them from the sequence. Let ~M~ be the largest difference of any two remaining numbers in the sequence, and ~m~ the smallest such difference. Select the ~K~ integers to be removed from ~V~ in such a way that the sum ~M+m~ is the smallest possible. Mirko isn't very good at math, so he has asked you to help him!

Input Specification

The first line of input contains two positive integers, ~N~ ~(3 \le N \le 1\,000\,000)~ and ~K~ ~(1 \le K \le N-2)~.

The second line of input contains ~N~ space-separated positive integers – the sequence ~V~ ~(-5\,000\,000 \le V_i \le 5\,000\,000)~.

Output Specification

The first and only line of output must contain the smallest possible sum ~M+m~.

Sample Input 1

5 2
-3 -2 3 8 6

Sample Output 1

7

Sample Input 2

6 2
-5 8 10 1 13 -1

Sample Output 2

13

Sample Input 3

6 3
10 2 8 17 2 17

Sample Output 3

6