Problem:
Score : 300 points

Problem Statement

"Pizza At", a fast food chain, offers three kinds of pizza: "A-pizza", "B-pizza" and "AB-pizza". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.

Nakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.

Constraints

1 ≤ A, B, C ≤ 5000

1 ≤ X, Y ≤ 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C X Y

Output

Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.

Sample Input 1

1500 2000 1600 3 2

Sample Output 1

7900

It is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.

Sample Input 2

1500 2000 1900 3 2

Sample Output 2

8500

It is optimal to directly buy three A-pizzas and two B-pizzas.

Sample Input 3

1500 2000 500 90000 100000

Sample Output 3

100000000

It is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.

Solution in OCaml (4.02.3) (judge verdict: Accepted)

open Batteries

let scan fmt f =
  Scanf.sscanf (read_line ()) fmt f

let scan_list cnv =
  read_line ()
  |> String.split_on_char ' '
  |> List.map cnv

let scan_array n m e conv =
  let arr = Array.make_matrix n m e in
  Enum.Labels.iter (0 --^ n)
    ~f:(fun i -> arr.(i) <- Array.of_list @@ scan_list conv);
  arr

let rec zip xs ys =
  match xs, ys with
  | [], _ -> []
  | _, [] -> []
  | x::xs, y::ys ->
    (x, y) :: zip xs ys

let dbg x = Printf.printf "%s\n" @@ dump x; x

let (a,b,c,x,y) = scan "%d %d %d %d %d" Tuple.Tuple5.make

let () =
  let n = min x y in
  let m = max x y in
  List.min [2*n*c+a*(x-n)+b*(y-n); a*x+b*y; 2*c*m]
  |> Printf.printf "%d\n"