Minimize System Cost

Remove exactly k contiguous elements; the remaining elements keep their original order, and the cost is the sum of the absolute differences between adjacent elements. Find the minimum cost.

输入格式

The first line contains n k (1≤k<n≤200000), and the second line contains n values (1..10⁹).

输出格式

Output a single integer answer.

样例 1

输入：

5 3
3 9 4 2 16

输出：

6

样例 2

输入：

2 1
1 9

输出：

0

样例 3

输入：

4 1
1 4 2 8

输出：

5

样例说明

Example 1: removing the last three elements leaves [3,9] with cost 6, smaller than the other two windows. Example 2: whichever element is removed, only one element remains, so the cost is 0. Example 3: removing the trailing 8 leaves [1,4,2] with cost 3+2=5; removing 4 gives 1+6=7, and no other option is better.