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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\ndef check(mid):\n time=0.0 \n for i in range(n):\n  if time<=arr[i]:\n   time=arr[i]+mid \n  elif time<=arr[i]+d:\n   time+=mid \n  else:\n   return False \n return True \n \nfor _ in range(int(input())):\n n,d=list(map(int,input().split()))\n arr=list(map(int,input().split()))\n arr.sort()\n low=0\n high=10000000000\n while ((high-low)>0.000001):\n  mid=low+(high-low)/2 \n  if check(mid):\n   ans=mid \n   low=mid \n  else:\n   high=mid\n print("{0:.6f}".format(ans)) \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13355