import itertools

def countArray(n,k,x):
  buildlis=[0]*(k+2)
  buildlis[0]=1
  buildlis[-1]=x
  t=1
  i=1

  while(t<k+1):
    buildlis[i]=t%(k+1)
    t+=1; i+=1



  #returns all possible combinations of numbers we need
  allperm=itertools.permutations(buildlis[1:-1], n-2)
  count=0;
  for perm in allperm:
    i=1; doub=False
    lis=list(perm)
    lis.insert(0,1)
    lis.insert(len(lis), x)
    #print(lis)

    while(i<n):
      if lis[i-1]==lis[i]:
        doub=True
        break #efficiecny
      i+=1
    if doub==False:
      print(lis) #let's see the ones that pass the criteria set
      count+=1

  return ("count array: ", count)

print(countArray(4,4,2))