-- All subsets of [0 .. n-1]
subsets :: Int -> [[Int]]
subsets 0 = [[]]
subsets n = let xs = subsets (n-1) in xs ++ [x ++ [n-1] | x <- xs]

-- Intersection.  Assume that two lists are sorted
intersection :: [Int] -> [Int] -> [Int]
intersection _ [] = []
intersection [] _ = []
intersection xs@(x:xs1) ys@(y:ys1)
  | x == y = x : intersection xs1 ys1
  | x < y  = intersection xs1 ys
  | x > y  = intersection xs ys1

-- Whether a lamp with spec (ks,p) is on when switched in xs are on
check :: (Int, [Int]) -> Int -> [Int] -> Bool
check (k, ss) p xs = length (intersection ss xs) `mod` 2 == p

-- Whether all lamps are on when switches in xs are on
all_on :: [(Int, [Int])] -> [Int] -> [Int] -> Bool
all_on lst_ks lst_p xs = and [check ks p xs | (ks, p) <- zip lst_ks lst_p]

solve :: Int -> Int -> [(Int, [Int])] -> [Int] -> Int
solve n m lst_ks lst_p
  = length (filter (all_on lst_ks lst_p) (subsets n))

parse_ks :: String -> (Int, [Int])
parse_ks str = let k : lst_s = map read (words str)
               in (k, map (+ (-1)) lst_s)   -- 1-indexed -> 0-indexed

main :: IO()
main = do
  cont <- getContents
  let line1 : line_rest = lines cont
      lines_ks = init line_rest
      line_p = last line_rest
      [s_n, s_m] = words line1
      n = read s_n
      m = read s_m
      lst_ks = map parse_ks lines_ks
      lst_p = map read (words line_p)
      answer = solve n m lst_ks lst_p
  putStrLn (show answer)
