let combinations combine l l' =
  CCList.cartesian_product [l; l']
  |> CCList.map (fun [p; p'] -> combine p p')

let paths xmax ymax =
  let rec aux x y prev_paths =
    if x > xmax || y > ymax then []
    else if x = xmax && y = ymax then prev_paths
    else
      let next_paths = List.flatten [
        aux (x+1)  y    [[ `Right ]];
        aux  x    (y+1) [[ `Down  ]];
      ] in
      combinations (@) prev_paths next_paths
  in
  aux 0 0 [[]]