BYTESM2  Philosophers Stone
One of the secret chambers in Hogwarts is full of philosopher’s stones. The floor of the chamber is covered by h × w square tiles, where there are h rows of tiles from front (first row) to back (last row) and w columns of tiles from left to right. Each tile has 1 to 100 stones on it. Harry has to grab as many philosopher’s stones as possible, subject to the following restrictions:
 He starts by choosing any tile in the first row, and collects the philosopher’s stones on that tile. Then, he moves to a tile in the next row, collects the philosopher’s stones on the tile, and so on until he reaches the last row.
 When he moves from one tile to a tile in the next row, he can only move to the tile just below it or diagonally to the left or right.
Input
The first line consists of a single integer T, the number of test cases. In each of the test cases, the first line has two integers. The first integer h (1 <= h <= 100) is the number of rows of tiles on the floor. The second integer w (1 <= w <= 100) is the number of columns of tiles on the floor. Next, there are h lines of inputs. The ith line of these, specifies the number of philosopher’s stones in each tile of the ith row from the front. Each line has w integers, where each integer m (0 <= m <= 100) is the number of philosopher’s stones on that tile. The integers are separated by a space character.
Output
The output should consist of T lines, (1 <= T <= 100), one for each test case. Each line consists of a single integer, which is the maximum possible number of philosopher’s stones Harry can grab, in one single trip from the first row to the last row for the corresponding test case.
Example
Input: 1 6 5 3 1 7 4 2 2 1 3 1 1 1 2 2 1 8 2 2 1 5 3 2 1 4 4 4 5 2 7 5 1 Output: 32 //7+1+8+5+4+7=32
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Akshay Aradhya:
20150718 22:28:48
Ahh.. DFS+DP :) Beautiful Problem 

Akshay Aradhya:
20150718 22:28:09
Got WA because of noob problems statement.One part of the problem says :


Obliterator:
20150717 18:57:42
This question is for educational purposes only. In fact, there was only one philosophers stone which was destroyed by Dumbledore to stop Voldemort from achieving immortality. 

ankit kumar:
20150704 06:10:38
@hareen your k value goes beyond testcases in printing answer


Amit Doshi:
20150703 11:46:34
Problem Setter, please correct the input format. I wasted half an hour over it inspite of getting correct solution. Its still not corrected. Cant even use Scanner class in Java. I did it btw.


hareesh:
20150702 06:37:56
can someone say me what is wrong with my code


ani_991:
20150628 17:06:20
Can't feel any better than this, my first DP ! :D 

r0bo_dart:
20150626 11:18:03
same as MISERMAN... after that try WPC4F ... By the way AC at a go :D 

vasayashwanth:
20150623 06:27:28
recursion causes TLE......just use memoization 

Marcin:
20150610 18:47:27
"""The integers are separated by a space character"""  it's not true. There are 1+ space characters between integers in the test cases. 
Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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