Minimize the heights
Submissions: 12583   Accuracy:

23.8%

  Difficulty: Medium   Marks: 4
       

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

 

** For More Input/Output Examples Use 'Expected Output' option **

Author: Rohan Malhotra


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