Chef received a permutation $P_1, P_2, \ldots, P_N$ and also an integer $D$ from his good friend Grux, because Grux was afraid he would forget them somewhere. However, since Grux was just playing with the permutation, it was all shuffled, and Chef only likes sorted permutations, so he decided to sort it by performing some swaps.
Chef wants to use the integer $D$ he just received, so he is only willing to swap two elements of the permutation whenever their absolute difference is exactly $D$. He has limited time, so you should determine the minimum number of swaps he needs to perform to sort the permutation, or tell him that it is impossible to sort it his way.

-----Input-----
- The first line of the 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 space-separated integers $N$ and $D$.
- The second line contains $N$ space-separated integers $P_1, P_2, \ldots, P_N$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum number of swaps, or $-1$ if it is impossible to sort the permutation.

-----Constraints-----
- $1 \le T \le 20$
- $1 \le N \le 200,000$
- $1 \le D \le N$
- $1 \le P_i \le N$ for each valid $i$
- $P_1, P_2, \ldots, P_N$ are pairwise distinct
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (20 points): $D = 1$
Subtask #2 (30 points):
- $N \le 1,000$
- the sum of $N$ over all test cases does not exceed $10,000$
Subtask #3 (50 points): original constraints

-----Example Input-----
2
5 2   
3 4 5 2 1
5 2    
4 3 2 1 5  

-----Example Output-----
3
-1

-----Explanation-----
Example case 1: Chef can perform the following swaps in this order:
- swap the first and fifth element
- swap the third and fifth element
- swap the second and fourth element

```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 = 't=int(input())\ndef solve(arr):\n if len(arr)==1:\n  return [0,arr]\n ans=0\n left=arr[:len(arr)//2]\n right=arr[len(arr)//2:]\n val1,lis1=solve(left)\n val2,lis2=solve(right)\n val,lis=merge(lis1,lis2)\n return [val+val1+val2,lis]\n\ndef merge(left,right):\n ans=[]\n final=0\n i,j=0,0\n n=len(left)\n while i<len(left) and j<len(right):\n  if left[i]<right[j]:\n   ans+=[left[i]]\n   i+=1\n  else:\n   ans+=[right[j]]\n   final+=n-i\n   j+=1\n ans+=left[i:]+right[j:]\n return [final,ans]\n  \n  \nfor _ in range(t):\n n,d=list(map(int,input().split()))\n arr=list(map(int,input().split()))\n ans=0\n dic={i:[] for i in range(d)}\n found=False\n for i in range(n):\n  if (arr[i]-i-1)%d!=0:\n   found=True\n   break\n  else:\n   if arr[i]%d==0:\n    dic[0]+=[arr[i]//d-1]\n   else:\n    dic[arr[i]%d]+=[(arr[i]-(arr[i]%d))//d]\n if found:\n  print(-1)\n else:\n  ans=0\n  for perm in list(dic.values()):\n   ans+=solve(perm)[0]\n  print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13487