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Given an array A[ ] denoting heights of N towers and a positive integer K, modify the heights of each tower either by increasing or decreasing them by K only once and then find out the minimum difference of the heights of shortest and longest towers.

Example

```
Input : A[] = {1, 15, 10}, k = 6
Output : 5
Explanation : We change 1 to 6, 15 to
9 and 10 to 4. Maximum difference is 5
(between 4 and 9). We can't get a lower
difference.
```

**Input**

The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains a positive integer K. The second line of each test case contains a positive integer N, denoting number of towers. The third line of the test cases contains N integers denoting the heights of N towers.

**Output**

For each test case in new line print out the minimum difference of heights possible.

**Constraints**

1 <= T <= 100

0 < K <= 30

0 < N <= 30

0 <= A[i] <= 500

**Examples **

**Input**

3

2

4

1 5 8 10

3

5

3 9 12 16 20

4

6

100 150 200 250 300 400

**Output**

5

11

292

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