You are given an array of N integers a1, a2, ..., aN and an integer K. Find the number of such unordered pairs {i, j} that 

- i ≠ j
- |ai + aj - K| is minimal possible

Output  the minimal possible value of |ai + aj - K| (where i ≠ j) and the number of such pairs for the given array and the integer K.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.

The first line of each test case consists of two space separated integers - N and K respectively.

The second line contains N single space separated integers - a1, a2, ..., aN respectively.

-----Output-----
For each test case, output a single line containing two single space separated integers - the minimal possible value of |ai + aj - K| and the number of unordered pairs {i, j} for which this minimal difference is reached.

-----Constraints-----

- 1 ≤ T ≤ 50
- 1 ≤ ai, K ≤ 109
- N = 2 - 31 point.
- 2 ≤ N ≤ 1000 - 69 points.

-----Example-----
Input:
1   
4 9
4 4 2 6

Output:
1 4

-----Explanation:-----
The minimal possible absolute difference of 1 can be obtained by taking the pairs of a1 and a2, a1 and a4, a2 and a4, a3 and a4.

```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\nfor _ in range(int(input())):\n n,k=map(int,input().split())\n list1=list(map(int,input().split()))\n list1.sort()\n min1=1000000000000001\n maxsum=0\n for i in range(len(list1)):\n  for j in range(i+1,len(list1)): \n   temp=abs(list1[i]+list1[j]-k) \n   if temp<min1:\n    min1=min(min1,temp)\n if min1!=0:        \n  cand1=k+min1\n  cand2=k-min1\n\n  s=list()\n  cnt=0\n  for i in list1:\n   t1=cand1-i\n   if t1 in s:\n    cnt+=s.count(t1)\n   t2=cand2-i\n   if t2 in s:\n    cnt+=s.count(t2)\n   s.append(i) \n  print(min1,cnt) \n else:\n  cand=k+min1\n  s=list()\n  cnt=0\n  for i in list1:\n   t1=cand-i\n   if t1 in s:\n    cnt+=s.count(t1)\n   s.append(i) \n  print(min1,cnt) '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13667