Since Max is wasting his time in his List I Communication credit lecture, he decided to start taking subsequences of arrays instead!

Specifically, he has $N$ integers, $A_i$, and wants to take a subsequence of length $K$, but to make his life even harder, his List I Communication credit professor adds a restriction: he must find the subsequence that has a length of $K$ with the minimum sum of the absolute difference between consecutive terms.

That is, he must minimize $|B_1-B_2|+|B_2-B_3|+\cdots +|B_{K-1}-B_K|$, where $B_i$ is the $i^{\text{th}}$ element of his subsequence and $|A-B|$ denotes the absolute difference between $A$ and $B$.

Can you find the minimum sum of absolute differences for every possible subsequence of length $K$?

Constraints

$2\le N\le 50000$

$2\le K\le min(100,N)$

$1\le A_i\le 50000$

Subtask 1 [40%]

$2\le N\le 1000$

Subtask 2 [60%]

No additional constraints.

Input Specification

The first line will contain two integers, $N$ and $K$, the array's length and the subsequence's length, respectively.

The second line will contain $N$ integers, $A_i$, the elements of the array.

Output Specification

Output the minimum sum of absolute differences between consecutive elements for any subsequence of length $K$.

Sample Input 1

6 2
1 5 6 2 1 3

Sample Output 1

0

Explanation for Sample 1

It can be proven that the minimal sum is achieved with the subsequence $[A_1=1,A_5=1]$.

Sample Input 2

6 4
3 2 6 2 7 9

Sample Output 2

6

Explanation for Sample 2

It can be proven that the minimal sum is achieved with the subsequence $[A_1=3,A_2=2,A_4=2,A_5=7]$.