You have a sequence $a$ with length $N$ created by removing some elements (possibly zero) from a permutation of numbers $(1, 2, \dots, N)$. When an element is removed, the length of the sequence doesn't change, but there is an empty spot left where the removed element was. You also have an integer $K$.
Let's call a permutation $p_1, p_2, \dots, p_N$ good if:
- it is possible replace empty spots in $a$ by numbers in such a way that we obtain the permutation $p$
- the number of positions $i$ ($1 < i \le N$) such that $p_i > p_{i-1}$ is equal to $K$
Your task is to find the number of good permutations.

-----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 $K$.
- The second line contains $N$ space-separated integers $a_1, a_2, \dots, a_N$. Each element of this sequence is either $0$ (indicating an empty spot previously occupied by a removed element) or an integer between $1$ and $N$ inclusive.

-----Output-----
For each test case, print a single line containing one integer — the number of good permutations.

-----Constraints-----
- $1 \le T \le 300$
- $0 \le K < N \le 8$
- each integer between $1$ and $N$ inclusive appears in $a$ at most once

-----Example Input-----
1
3 1
2 0 0

-----Example Output-----
2

-----Explanation-----
Example case 1: The two possible good permutations are $(2,3,1)$ and $(2,1,3)$.

```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 = 'from itertools import permutations\n\nfor _ in range(int(input())):\n N,K=list(map(int,input().split()))\n arr=list(map(int,input().split()))\n arr1=[]\n arr2=[]\n for i in range(1,len(arr)+1):\n  arr1.append(i)\n indexzero=[]\n for i in range(0,len(arr)):\n  if(arr[i]==0):\n   indexzero.append(i)\n  else:\n   arr2.append(arr[i])\n # arr3 = [x for x in arr1 if x not in arr2]\n arr3= list(set(arr1)-set(arr2))\n result=permutations(arr3)\n perm=[]\n for i in result:\n  perm.append(i)\n step=0\n count=0\n for p in range(0,len(perm)):\n  temp=[]\n  for q in range(0,len(arr)):\n   if(arr[q]==0):\n    temp.append(perm[p][step])\n    step+=1 \n   else:\n    temp.append(arr[q])\n  k=0\n  step=0\n  for m in range(0,len(temp)-1):\n   if(temp[m]<temp[m+1]):\n    k+=1\n  if(k==K):\n   count+=1 \n print(count)\n   \n    \n  \n \n  \n \n   \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13853