Problem of the day
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 ‘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.
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'.
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.
You are not required to print the expected output, and it has already been taken care of. Just implement the function.
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
3
2 1
5 2
1 2
3
4 3
5 5 5 5
1
0
0
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.
3
2 10
1 2
4 8
1 2 3 4
3 2
2 4 6
1
3
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.