A16163. Balanced Round

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?

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 $2 \cdot 10^5$ .

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.

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 $10$ .