import "prelude.eg"

using System
using List

data open, closed

def toggle =
    [ open N -> closed N | closed N -> open N ]

def doors =
    [ N -> map [ N -> closed N ] (fromto 1 N) ]

def toggleK =
    [ K, nil            -> nil
    | K, cons (D N) DD  ->
         let DOOR = if (N%K) == 0 then toggle (D N) else D N in
             cons DOOR (toggleK K DD) ]