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FatMouse has stored some cheese in a city. The city can be considered as a square grid of dimension n: each grid location is labelled (p,q) where 0 <= p < n and 0 <= q < n. At each grid location Fatmouse has hid between 0 and 100 blocks of cheese in a hole. Now he's going to enjoy his favorite food. 

FatMouse begins by standing at location (0,0). He eats up the cheese where he stands and then runs either horizontally or vertically to another location. The problem is that there is a super Cat named Top Killer sitting near his hole, so each time he can run at most k locations to get into the hole before being caught by Top Killer. What is worse -- after eating up the cheese at one location, FatMouse gets fatter. So in order to gain enough energy for his next run, he has to run to a location which have more blocks of cheese than those that were at the current hole. 

Given n, k, and the number of blocks of cheese at each grid location, compute the maximum amount of cheese FatMouse can eat before being unable to move. 

InputThere are several test cases. Each test case consists of 

a line containing two integers between 1 and 100: n and k 
n lines, each with n numbers: the first line contains the number of blocks of cheese at locations (0,0) (0,1) ... (0,n-1); the next line contains the number of blocks of cheese at locations (1,0), (1,1), ... (1,n-1), and so on. 
The input ends with a pair of -1's. 
OutputFor each test case output in a line the single integer giving the number of blocks of cheese collected. 
Sample Input

3 1
1 2 5
10 11 6
12 12 7
-1 -1

Sample Output

37

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

#define MAXN 101
/*
可以向一个方向最多移动k步
因为从一个位置进入所获得的收益是固定的和前面的状态没有关系，所以可以把这个结果记录下来节省时间

记忆化搜索 递归
在上下左右四个方向找 受益最大的格子同时记录
*/
int n,k,g[MAXN][MAXN],dp[MAXN][MAXN];
int dir[4][2] = {{1,0},{-1,0},{0,1},{0,-1}};
int Mdfs(int x,int y)
{
    if(dp[x][y])
        return dp[x][y];
    int Max = 0;
    for(int i=0;i<4;i++)
    {
        for(int d=1;d<=k;d++)
        {
            int nx = x + dir[i][0]*d;
            int ny = y + dir[i][1]*d;
            if(nx<n&&nx>=0&&ny>=0&&ny<n&&g[nx][ny]>g[x][y])
                Max = max(Max,Mdfs(nx,ny));
        }
    }
    dp[x][y] = Max + g[x][y];
    return dp[x][y];
}
int main()
{
    while(scanf("%d%d",&n,&k))
    {
        if(n==-1&&k==-1) break;
        memset(dp,0,sizeof(dp));    
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
                scanf("%d",&g[i][j]);
        }
        printf("%d
",Mdfs(0,0));
    }
    return 0;
}