Balanced Round

2000ms

262144K

Description:

You 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?

Input:

The 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 $$$2 \cdot 10^5$$$.

Output:

For each test case, output a single integer — the minimum number of problems you have to remove so that an arrangement of problems is balanced.

Sample Input:

7
5 1
1 2 4 5 6
1 2
10
8 3
17 3 1 20 12 5 17 12
4 2
2 4 6 8
5 3
2 3 19 10 8
3 4
1 10 5
8 1
8 3 1 4 5 10 7 3

Sample Output:

Note:

For 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 $$$10$$$.

Informação

Provedor Codeforces

Código CF1850D