[USACO14MAR] The Lazy Cow S

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 ```cpp 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。

\* Line 1: The integers N and K. \* Lines 2..1+N: Line r+1 contains N integers describing row r of the grid.

\* 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

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