(*
let rec binary n =
  if (n = 0) then []
  else (n mod 2)::(binary (n / 2));;
*)
let binary n = unfoldr (fun x -> x = 0) (fun x -> x mod 2) (fun x -> x / 2) n

(*
let rec decimal b =
  match b with
  [] -> 0
  | x::xs -> x + 2 * (decimal xs)
*)
let decimal b = foldr (fun x y -> x + 2 * y) 0 b

let rec pow m n = if n = 0 then 1 else m * (pow m (n - 1))

(* calculate m^{bn} *)
let fastpow m bn = foldr (fun x y -> y * y * if x = 1 then m else 1) 1 bn