import Html exposing (Html, button, div, text)
import Html.Events exposing (onClick)

main =
  Html.beginnerProgram { model = model, view = view, update = update }

type alias Model =
    { nbr : Int
    , dec : List Int
    }

model : Model
model = Model 0 []

type Msg = Increment | Decrement | Decompose

update : Msg -> Model -> Model
update msg model =
  case msg of
    Increment ->
      { model | nbr = model.nbr + 1 }

    Decrement ->
      { model | nbr = model.nbr - 1 }

    Decompose ->
      { model | dec = decompose model.nbr 2 []}

decompose : Int -> Int -> List Int -> List Int
decompose nbr factor list =
    if (nbr > 0 && sqrt(toFloat nbr) >= toFloat factor) then
        if ((nbr % factor) == 0) then
            decompose (nbr//factor) factor (factor :: list)
        else
            decompose nbr (factor + 1) list
    else
        nbr :: list

view : Model -> Html Msg
view model =
  div []
    [ button [ onClick Decrement ] [ text "-" ]
    , button [ onClick Increment ] [ text "+" ]
    , button [ onClick Decompose ] [ text "Dec" ]
    , div [] [ text (toString model.nbr) ]
    , div [] [ text ("Decomposition : " ++ toString model.dec) ]
    ]