Problem Statement: Minimize the Maximum

You are given an array of integers and an integer K. For each array element, you can adjust it by increasing or decreasing it by a value of K. Your goal is to minimize the difference between the maximum and minimum elements of the array after these modifications.

Input:

The first line of input contains an integer T, denoting the number of test cases.
 For each test case:
 The first line contains an integer N, the number of elements in the array.
 The second line contains N integers representing the elements of the array.
 The third line contains an integer K.

Output:

For each test case, output the minimum possible difference between the maximum and minimum elements of the array after modifications.

Example:

Input:

2
4
1 5 8 10
2
3
3 9 12
4

Output:

5
5

Constraints:

• 1 <= T <= 5
• 1 <= N <= 10^5
• 0 <= arr[i] <= 10^5
• 0 <= K <= 10^5
• Time limit: 1 second

Note:

You are not required to print the output. Just return the answer.