**Problem C**

**Chopsticks**

**Input:** Standard Input

**Output:** Standard Output

In China, people use a pair of chopsticks to get food on the table, but Mr. L is a bit different.
He uses a set of three chopsticks -- one pair, plus an EXTRA long chopstick to get some big food by
piercing it through the food.
As you may guess, the length of the two shorter chopsticks should be as close as possible, but the
length of the extra one is not important, as long as it's the longest. To make things clearer,
for the set of chopsticks with lengths A,B,C(A<=B<=C), (A-B)^{2} is called the 'badness' of the set.

It's December 2nd, Mr.L's birthday! He invited K people to join his birthday party, and would like to introduce his way of using chopsticks. So, he should prepare K+8 sets of chopsticks(for himself, his wife, his little son, little daughter, his mother, father, mother-in-law, father-in-law, and K other guests). But Mr.L suddenly discovered that his chopsticks are of quite different lengths! He should find a way of composing the K+8 sets, so that the total badness of all the sets is minimized.

**Input**

The first line in the input contains a single integer T, indicating the
number of test cases(1<=T<=20).
Each test case begins with two integers K, N(0<=K<=1000,
3K+24<=N<=5000), the number of guests and the number of
chopsticks.
There are N positive integers L_{i} on the next line in non-decreasing order indicating the lengths of the chopsticks.(1<=L_{i}<=32000).

**Output**

For each test case in the input, print a line containing the minimal total badness of all the sets.

**Hints**

- clearly, it only makes sense to consider adjacent pairs as "short" pairs
- a good subproblem is: what is the minimum total "badness" for K' chopstick sets (K' <= K) chosen from chopsticks i..N?
- the strategy is: for each chopstick, try pairing it with its neighbour, or discarding it
- you don't need to explicitly find out which chopsticks you will use as "long". You just need to make sure that there will be enough sufficiently long chopsticks, so you have to be a little careful when discarding chopsticks.
- the actual solution is very short

**Sample Input**

1 40

1 8 10 16 19 22 27 33 36 40 47 52 56 61 63 71 72 75 81 81 84 88 96 98 103 110 113 118 124 128 129 134 134 139 148 157 157 160 162 164

**Sample Output**

**Note**

8,10,16; 19,22,27; 61,63,75; 71,72,88; 81,81,84; 96,98,103; 128,129,148; 134,134,139; 157,157,160

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Rujia Liu