题目描述

Unhappy with the poor health of his cows, Farmer John enrolls them in an assortment of different physical fitness activities. His prize cow Bessie is enrolled in a running class, where she is eventually expected to run a marathon through the downtown area of the city near Farmer John's farm!

The marathon course consists of N checkpoints (3 <= N <= 500) to be visited in sequence, where checkpoint 1 is the starting location and checkpoint N is the finish. Bessie is supposed to visit all of these checkpoints one by one, but being the lazy cow she is, she decides that she will skip up to K checkpoints (K < N) in order to shorten her total journey. She cannot skip checkpoints 1 or N, however, since that would be too noticeable.

Please help Bessie find the minimum distance that she has to run if she can skip up to K checkpoints.

Since the course is set in a downtown area with a grid of streets, the distance between two checkpoints at locations (x1, y1) and (x2, y2) is given by |x1-x2| + |y1-y2|.

Bessie 参加城市马拉松比赛，要顺序经过 $N (3 \leq N \leq 500)$ 个检查点，其中检查点 $1$ 是起点，检查点 $N$ 是终点。 Bessie尝试略过 $K(K < N)$ 个检查点，以减少总路程，检查点 $1$ 和检查点 $N$ 不能被略过。两个检查点的距离是 $|x_1-x_2| + |y_1-y_2|$。

输入输出格式

输入格式

The first line gives the values of N and K.

The next N lines each contain two space-separated integers, x and y,representing a checkpoint (-1000 <= x <= 1000, -1000 <= y <= 1000).

The checkpoints are given in the order that they must be visited.

Note that the course might cross over itself several times, with several checkpoints occurring at the same physical location. When Bessie skips such a checkpoint, she only skips one instance of the checkpoint -- she does not skip every checkpoint occurring at the same location.

输出格式

Output the minimum distance that Bessie can run by skipping up to K checkpoints. In the sample case shown here, skipping the checkpoints at (8, 3) and (10, -5) leads to the minimum total distance of 4.

5 2
0 0
8 3
1 1
10 -5
2 2

4