题目描述

It's a hot summer day, and Bessie the cow is feeling quite lazy. She wants

to locate herself at a position in her field so that she can reach as much

delicious grass as possible within only a short distance.

The field Bessie inhabits is described by an N by N grid of square cells

(1 <= N <= 400). The cell in row r and column c (1 <= r,c <= N) contains

G(r,c) units of grass (0 <= G(r,c) <= 1000). From her initial square in

the grid, Bessie is only willing to take up to K steps (0 <= K <= 2*N).

Each step she takes moves her to a cell that is directly north, south,

east, or west of her current location.

For example, suppose the grid is as follows, where (B) describes Bessie's

50    5     25*   6     17    
14    3*    2*    7*    21    
99*   10*   1*(B) 2*    80*    
8     7*    5*    23*   11   
10    0     78*   1     9        

initial position (here, in row 3, column 3):

If K=2, then Bessie can only reach the locations marked with *s.

Please help Bessie determine the maximum amount of grass she can reach, if

she chooses the best possible initial location in the grid.

奶牛贝茜非常懒惰，她希望在她的地盘内找到一点最佳位置居住，以便在有限的步数内可以吃到尽量多的青草。

她的地盘是一个 $N \times N(1\le N \le 400)$ 的矩阵，第 $r$ 行 $c$ 列包含 $G(r,c)$ 单位的青草 $(0 \le G(r,c) \le 1000)$。从她的居住点，她最多愿意走 $K$ 步 $(0 \le K \le 2 \times N)$，每一步她可以走到上与她相邻的某个格子。

输入格式

* Line 1: The integers N and K.

* Lines 2..1+N: Line r+1 contains N integers describing row r of the

grid.

输出格式

* Line 1: The maximum amount of grass Bessie can reach, if she chooses

the best possible initial location (the location from which

she can reach the most grass).

5 2
50 5 25 6 17
14 3 2 7 21
99 10 1 2 80
8 7 5 23 11
10 0 78 1 9

342

提示

OUTPUT DETAILS:

In the example above, Bessie can reach 342 total units of grass if she

locates herself in the middle of the grid.

Source: USACO 2014 March Contest, Silver