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Problem

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Chocolates With Magical Number

Contributed by

Amit Priyankar

Last Updated: 23 Feb, 2023

Easy

0/40

Avg time to solve 10 mins

Success Rate 90 %

3 upvotes

Problem Statement

Ninja is planning to give ‘PACKET’ of 'N' chocolates to his friend on his birthday. Each chocolate in ‘PACKET’ has a non-negative sweetness level that denotes how sweet the chocolate is. He wants to give these chocolates to his friend such that the absolute difference between chocolate with maximum sweetness and minimum sweetness should be as minimum as possible.

In order to do this, Ninja uses a magic number, 'K' under the following conditions:

1. Using this magical number, Ninja can either increase or decrease the sweetness of each chocolate. 
2. After increasing or decreasing the sweetness, all the new sweetness values must be non-negative. 
3. Ninja must use this magic number on each chocolate exactly once.

For Example :

For ‘PACKETS’ = [1, 2, 3, 4, 5] and 'K' =  1, the absolute difference between two chocolates with maximum (5) and minimum (1) sweetness is 4. Now in order to minimize this value, Ninja increases [1, 2, 3] and decreases [4, 5] by 1 (‘K’ = 1). So, ‘PACKET’ becomes [2,3,4,3,4]. Now, the absolute difference between the two chocolates with maximum (4) and minimum (2) sweetness is 2 which is the minimum possible.

As Ninja is busy preparing for the party, he asks you for help. Can you help Ninja determine the minimum possible difference between the maximum and minimum sweetness of chocolates in 'PACKET’ after using the magic number 'K'?

Detailed explanation ( Input/output format, Notes, Images )

Input Format :

The first line contains an integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow.

The first line of each test case contains two single space-separated integers 'N' and 'K' denoting the number of chocolates in the 'PACKET' and the magic number, respectively.

The second line of each test case contains 'N' single space-separated integers, denoting the sweetness of each chocolate in 'PACKET'.

Output Format :

For each test case, print the minimum possible difference between the maximum and minimum sweetness value of chocolates in the array/list ‘PACKET’.

Print the output of each test case in a separate line.

Note :

You are not required to print the expected output, and it has already been taken care of. Just implement the function.

Constraints :

1 <= T <= 100
1 <= N <= 10^5
1 <= K <= 10^5
1 <= PACKET[i] <= 10^5

Where 'T' is the number of test cases, 'N' denotes the number of chocolates in the given array/list 'PACKET' and 'K' denotes the given magic number, respectively. 'PACKET[i]' denotes the sweetness of the i'th chocolate. 

Time Limit : 1 sec

Sample Input 1 :

Sample Output 1 :

1
0
0

Explanation of Sample Input 1 :

For the first test case:
Given ‘K’ = 1 so, [6, 3], [6, 1], [4, 1] and [4, 3] are all the possible ways in which sweetness of chocolates can be increased or decreased among which [4,3] has the least difference of 1 between the minimum and maximum sweetness value.   

For the second test case :
Given ‘K’ = 2 so [5] and [1] are the only possible ways in which the sweetness of chocolates can be increased or decreased and the minimum difference between the minimum and maximum sweetness value obtained in both ways is 0.   

For the third test case:
Given ‘K’ = 3 and all the elements of ‘PACKET’ are the same. Among all possible ways of increasing or decreasing sweetness values of chocolates by ‘K’, [8, 8, 8, 8] and [2, 2, 2, 2] are the only possible ways which yield a minimum difference of 0 in the maximum and minimum sweetness values.

Sample Input 2 :

Sample Output 2 :

1
3
2

Explanation of Sample Input 2 :

For the first test case:
Given ‘K’ = 10 so we can only increase the sweetness of all chocolates in ‘PACKET’ by ‘K’ because the sweetness of chocolates must be positive. We get [11,12] after modifying the ‘PACKET’. So, the least difference in the maximum and minimum sweetness values is 1. 

For the second test case:
Given ‘K’ = 8 so we can only increase the sweetness of all chocolates in ‘PACKET’ by ‘K’ because the sweetness of chocolates must be positive. We get [9,10,11,12] after modifying the ‘PACKET’. So, the least difference in the maximum and minimum sweetness values is 3.    

For the third test case :
Among all possible ways of increasing or decreasing the sweetness of chocolates in the given ‘PACKET’ by ‘K’, [4,2,4] and [4,6,4] are the optimal chocolate sweetness obtained which have the least difference of 2 between the maximum and the minimum sweetness values among all possibilities.

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