let rec pow a = function
  | 0 -> 1
  | 1 -> a
  | n ->
    let b = pow a (n / 2) in
    b * b * (if n mod 2 = 0 then 1 else a)

let rec powmod a d = function
  | 0 -> 1
  | 1 -> a mod d
  | n ->
    let b = (powmod a d (n / 2)) mod d in
    (((b * b) mod d) * (if n mod 2 = 0 then 1 else a)) mod d

let int_and a b =
  match (a>0, b>0) with
    true, true -> 1
  | _, _ -> 0

let int_or a b =
  match (a>0, b>0) with
    false, false -> 0
  | _, _ -> 1

let int_eq a b =
  if a = b then 1 else 0

let int_less a b =
  if a < b then 1 else 0

let int_less_eq a b =
  if a <= b then 1 else 0

let int_more a b =
  if a > b then 1 else 0

let int_more_eq a b =
  if a >= b then 1 else 0

let int_not a =
  if a > 0 then 0 else 1

let rec fromIntToString (alphabet: string) (x: int) : string =
  let base = String.length alphabet in
  if x < 0 then
    ""
  else if x < base then
    String.get alphabet x |> String.make 1
  else
    (fromIntToString (alphabet) (x/base - 1)) ^ (String.get alphabet (x mod base) |> String.make 1)