fun hailstone_step(x: int): int =
  if (x % 2) == 0
  then x/2
  else (3*x) + 1

fun hailstone_seq(x: int): []int =
  let capacity = 100
  let i = 1
  let steps = replicate capacity (-1)
  let steps[0] = x
  loop ((capacity,i,steps,x)) = while x != 1 do
    let (steps, capacity) =
      if i == capacity then
        (concat steps (replicate capacity (-1)),
         capacity * 2)
      else (steps, capacity)
    let x = hailstone_step x
    let steps[i] = x
    in (capacity, i+1, steps, x)
  in #1 (split i steps)

fun hailstone_len(x: int): int =
  let i = 1
  loop ((i,x)) = while x != 1 do
    (i+1, hailstone_step x)
  in i

fun max (x: int) (y: int): int = if x < y then y else x

fun main (x: int) (n: int): ([]int, int) =
  (hailstone_seq x,
   reduce max 0 (map hailstone_len (map (1+) (iota (n-1)))))