### 2312: Image Recognition

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The monitoring  system  without any person does not necessarily require a large number of dynamic images. It is enough to transport an immobile image in ** seconds in most practical condition.
In the JD-T warehouse, the goods is stored in large cubical crates, all of which have the same dimensions. The crates are stacked in neat piles, forming a three-dimensional grid. The remote online monitoring system takes pictures of the piles once in S seconds using three cameras: a front camera, a side camera and a top camera. The image from the front camera shows the height of the tallest pile in each column, the image from the side camera shows the height of the tallest pile in each row, and the image from the top camera shows whether or not each pile is empty. If the monitoring system detects a change in any of the images, it sounds an alarm.

Figure I-1 shows a possible layout of the grid and the image from each of the cameras.

Figure I-2 , I-3 and figure I-1 have the same images from each of the cameras.

A theft gang noticed this unmanned warehouse. They found that it took T seconds to transport a crate. They wants to steal as many crates as possible. Since they cannot disable the monitoring system, they plans to fool it by arranging the remaining crates into piles so that the next set of camera images are the same.

Is the remote online monitoring system safe?  If it's not safe, the maximum number of crates that can be stolen while leaving a configuration of crates that will fool the monitoring system, camera images remain unchanged.

The first line of the input contains one integer T, which is the number of  test cases (1<=T<=6).  Each test case specifies:

* Line 1:    S  T      (1<=S=1012  1<=T=10)

* Line 2:    m  n     rows and columns in the grid, respectively. (1<=m, n<=100)

*Line 3..m+3:  each line contains n integers, the heights (in crates) of  the piles in the corresponding row.  (  all heights are between 0 and 109 inclusive.)

For each test case , print the maximum number of crates that can be stolen without being detected.

3
10000 100
5 5
1 4 0 5 2
2 1 2 0 1
0 2 3 4 4
0 3 0 3 1
1 2 2 1 1
10000 100
2 3
50 20 3
20 10 3
1000 99
2 3
50 20 3
20 10 3


9
30
10