Minimize the Maximum

You are given an array of N integers and an integer K. For each array element, you are allowed to increase or decrease it by a value k. The task is to minimize the difference between the maximum element and the minimum element after modifications.

Input Format :

The first line of input contains a single integer T, representing the number of test cases or queries to be run. 
Then the test cases follow.

The first line of each test case contains a positive integer N which represents the number of elements of an array.

The Second line of each test case contains N integers denoting the elements of the array.

The third line of each test case contains a positive integer K.

Output Format :

For each test case, return the minimum difference between the maximum element and minimum element of the array by either increasing or decreasing elements of the array by K.

Note:

You do not need to print anything. It has already been taken care of.

Constraints :

1 <= T <= 5
1 <= N <= 10^5
0 <= arr[i] <= 10^5
0 <= K <= 10^5

Time limit = 1 sec

Sample Input 1 :

1
3
1 15 10
6

Sample Output 1:

5

Explanation of Input 1 :

Arrays that can be obtained by either increasing or decreasing each elements by k are
[-5 9 4]   difference between maximum and minimum is 16
[-5 9 16] difference between maximum and minimum is 21
[-5 21 16] difference between maximum and minimum is 26
[-5 21 4] difference between maximum and minimum is 26
[7 9 4]   difference between maximum and minimum is 5
[7 9 16] difference between maximum and minimum is 9
[7 21 16] difference between maximum and minimum is 14
[7 21 4] difference between maximum and minimum is 17
So the minimum of all differences between maximum and minimum elements is 5. So, we need to return 5.

Sample Input 2 :

1
3
1 2 3 
2

Sample Output 2:

2