Solve the programming task below in a Python markdown code block.
There are N events (numbered from 1 to N) and M contestants (numbered from 1 to M). For each event i, contestant j receives a predetermined number of points A_{i, j}.

A [subset] of these events will be selected, and the final score of contestant j, denoted s_{j}, will be the sum of their points for each event selected.

Formally, if S denotes the set of events chosen, then \displaystyle s_{j} = \sum_{x \in S} A_{x, j} for each 1 ≤ j ≤ M. If S is empty, we define s_{j} = 0 for each j.

The *differentiation* of the final scoreboard is equal to

\max_{i=1}^M (\sum_{j=1}^M |s_{j} - s_{i}|)

Find the maximum possible differentiation over all subsets of events. 

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of several lines.
- The first line of each test case contains two space-separated integers N and M — the number of events and contestants, respectively.
- The next N lines describe the events. The i-th of these N lines contains M space-separated integers A_{i, 1}, A_{i, 2}, \ldots, A_{i, M} — the j-th of which describes the number of points the j-th contestant earns for event i.

------ Output Format ------ 

For each test case, output on a new line the maximum differentiation over all subsets of events.

------ Constraints ------ 

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$1 ≤ M ≤ 10^{5}$
$0 ≤ A_{i, j} ≤ 10^{5}$
- The sum of $N\cdot M$ over all test cases won't exceed $10^{5}$.

----- Sample Input 1 ------ 
3
1 1
1
3 3
1 0 1
1 2 1
1 2 1
4 2
1 3
5 1
6 8
2 1

----- Sample Output 1 ------ 
0
4
5
----- explanation 1 ------ 
Test case $1$: There are two possible subsets of events — either take the only event, or don't. In either case, the differentiation will be $0$.

Test case $2$: Take events $2$ and $3$ for a final scoreboard of $(2, 4, 2)$. The differentiation of this scoreboard is $4$, and it can be proven that this is the maximum.

Test case $3$: Take events $3$ and $5$, for a final scoreboard of $(7, 2)$, which has a differentiation of $5$.