output_description: Print the number of ways to select cards such that the average of the written
  integers is exactly A.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N A
      x_1 x_2 ... x_N
attempt: def app(numlist, A):
      counter = 0
      N = len(numlist)
      for i in range(1, N):
          counter += f(numlist, i, A * i)
      return counter
  
  
  def f(numlist, rest, sum):
      result = 0
      numset = set(numlist)
      if rest == 1:
          return numlist.count(sum)
  
      elif rest == 2:
          for big in numset:
              if (sum - big in numset) and (big >= sum - big):
                  result += counter(numlist, big, sum - big)
          return result
      else:
          for i in numset:
              i_place = numlist.index(i)
              result += f(numlist[i_place + 1 :], rest - 1, sum - i)
          return result
  
  
  def counter(numlist, big, small):
      hist = mkhist(numlist)
      if big == small:
          N = hist[big]
          return N * (N - 1) / 2
      else:
          big_N = hist[big]
          small_N = hist[small]
          return big_N * small_N
  
  
  def mkhist(numlist):
      hist = dict()
      for char in numlist:
          if not char in hist.keys():
              hist[char] = 1
          else:
              hist[char] += 1
      return hist
  
  
  N, A = input()
  inputs = input()
  
  inputnum = map(int, inputs.split(" "))
  inputnum = sorted(list(inputnum))
  print(app(inputnum, A))
  
problem_description: Statement
  
  Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i.
  He is selecting one or more cards from these N cards, so that the average of
  the integers written on the selected cards is exactly A. In how many ways can
  he make his selection?
samples: [{"input": "4 8\n    7 9 8 9", "output": "5\n    \n\n  * The following are the 5 ways to select cards such that the average is 8:\n    * Select the 3-rd card.\n    * Select the 1-st and 2-nd cards.\n    * Select the 1-st and 4-th cards.\n    * Select the 1-st, 2-nd and 3-rd cards.\n    * Select the 1-st, 3-rd and 4-th cards.\n\n* * *"}, {"input": "3 8\n    6 6 9", "output": "0\n    \n\n* * *"}, {"input": "8 5\n    3 6 2 8 7 6 5 9", "output": "19\n    \n\n* * *"}, {"input": "33 3\n    3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3", "output": "8589934591\n    \n\n  * The answer may not fit into a 32-bit integer."}]