import Data.Tuple
import Data.List
import Data.Ord

data Tree a = Node a (Tree a) (Tree a)
memoize f = memof where memof = f (query (blank memof))
blank f = blank' 1 where blank' k = Node (f k) (blank' (2*k)) (blank' (2*k+1))

query m x = query' m bits
 where
  bits = reverse (take w (unfoldr (return . swap . flip divMod 2) x))
  w = floor (logBase 2 (fromIntegral x))
  query' (Node v left right) bs
   | bs == [] = v
   | head bs == 0 = query' left (tail bs)
   | otherwise = query' right (tail bs)

combBy :: Integer -> [a] -> [[a]]
combBy 0 _ = [[]]
combBy _ [] = []
combBy n (x:xs) = map (x:) (combBy (n-1) xs) ++ combBy n xs

main = do
 [h,w,k,p] <- map read . words <$> getLine
 xyns <- map ((\[x,y,n] -> ((read x, read y),n)) . words) . lines <$> getContents
 let (r,fs) = japari (h+1) (w+1) k p xyns
 print (mod r (10^9+7))
 mapM_ putStrLn fs

japari :: Integer -> Integer -> Integer -> Integer -> [((Integer,Integer),String)] -> (Integer, [String])
japari h w k p xyns = (route h w (map (pos.fst) left) 0, (map snd xyns) \\ (map snd left))
 where
  left = maximumBy (comparing (\fs -> route h w (map (pos.fst) fs) 0)) (combBy (k-p) xyns)
  pos (x,y) = y*h + x

route h w fs = memoize $ 
 \f n -> 
  if isFriend n then 0 else
  if isGoal n then 1 else
  if isNB n then f (n+1) else
  if isEB n then f (n+h) else f (n+1) + f (n+h)
 where
  isGoal n = n == h*w-1
  isNB n = div n h == w-1
  isEB n = mod n h == h-1
  isFriend n = elem n fs