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, $N$ $(3\le N\le 1000000)$ and $K$ $(1\le K\le N-2)$.

The second line of input contains $N$ space-separated positive integers – the sequence $V$ $(-5000000\le V_i\le 5000000)$.

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