D. Balanced Roundtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are the author of a Codeforces round and have prepared n problems you are going to set, problem i having difficulty a_i. You will do the following process:   remove some (possibly zero) problems from the list;  rearrange the remaining problems in any order you wish. A round is considered balanced if and only if the absolute difference between the difficulty of any two consecutive problems is at most k (less or equal than k).What is the minimum number of problems you have to remove so that an arrangement of problems is balanced?InputThe first line contains a single integer t (1 \leq t \leq 1000) — the number of test cases.The first line of each test case contains two positive integers n (1 \leq n \leq 2 \cdot 10^5) and k (1 \leq k \leq 10^9) — the number of problems, and the maximum allowed absolute difference between consecutive problems.The second line of each test case contains n space-separated integers a_i (1 \leq a_i \leq 10^9) — the difficulty of each problem.Note that the sum of n over all test cases doesn't exceed 2 \cdot 10^5.OutputFor each test case, output a single integer — the minimum number of problems you have to remove so that an arrangement of problems is balanced.ExampleInput
75 11 2 4 5 61 2108 317 3 1 20 12 5 17 124 22 4 6 85 32 3 19 10 83 41 10 58 18 3 1 4 5 10 7 3Output
2
0
5
0
3
1
4
NoteFor the first test case, we can remove the first 2 problems and construct a set using problems with the difficulties [4, 5, 6], with difficulties between adjacent problems equal to |5 - 4| = 1 \leq 1 and |6 - 5| = 1 \leq 1.For the second test case, we can take the single problem and compose a round using the problem with difficulty 10.
75 11 2 4 5 61 2108 317 3 1 20 12 5 17 124 22 4 6 85 32 3 19 10 83 41 10 58 18 3 1 4 5 10 7 3
2 0 5 0 3 1 4 
['brute force', 'greedy', 'implementation', 'sortings', '*900']