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# Minimize The Maximum

Difficulty: EASY
Avg. time to solve
15 min
Success Rate
85%

Problem Statement

#### 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 For Sample Input 1 :
``````Arrays that can be obtained by either increasing or decreasing each element 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
``````   Console