Chef is the leader of Chef's Earth Defense Organization, and his mission is to counter aliens which are threatening the earth. According to information gathered by the organization, there are $N$ alien spaceships (numbered $1$ through $N$) planning to invade the earth. The $i$-th spaceship will appear on the radar at time $C_i$. Each spaceship needs $D$ time to reach earth once it appears on the radar.
Chef's organization owns a huge laser cannon which can destroy one spaceship in one shot. However, once the cannon is used once it needs some amount of cool-down time in order to be used again (first shot doesn't require cool-down time before it is used). This cool-down time, however, is configurable. It has to be set before the first shot, and cannot be changed after that. If Chef sets a lower cool-down time, that would increase the energy consumed by the cannon, and vice-versa - the higher the cool-down time, the lower the energy consumed.
This might be a long battle, and Chef wants to use as little energy as possible. So Chef wants to maximize the cool-down time while still being able to destroy all spaceships before any of them arrive on earth. In particular, the $i$-th spaceship should be shot between the times $C_i$ and $C_i + D$ (both end points inclusive).

-----Input:-----
- The first line of input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two integers $N$ and $D$.
- The second line contains $N$ space-separated integers $C_1, C_2, \ldots, C_N$.

-----Output:-----
For each test case, print a single line containing one real number― the maximum cool-down time possible. Your answer will be considered correct if the absolute or relative error of the answer does not exceed $10^{-6}$.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq N \leq 10^5$
- $1 \leq C_i \leq 10^9$ for each valid $i$
- $1 \leq D \leq 10^9$
- The sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $N \le 1,000$
- the sum of $N$ over all test cases does not exceed $10,000$
Subtask #2 (50 points): Original constraints

-----Sample Input:-----
2
3 2
3 2 3
2 1
5 6

-----Sample Output:-----
1.5000000000
2.0000000000

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