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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use v5.10;
use List::Util qw/max min/;
use POSIX      qw/ceil/;

my ($a, $b, $c, $x, $y) = split(/[ \n]+/, <>);
#say join(",", $a, $b, $c, $x, $y); #debug

$naive  = $a * $x + $b * $y;
$all_ab = max($x, $y) * 2 * $c;
if ($x < $y) {
  $a_b_ab = $x * 2 * $c + ceil(($y - $x) / 2) * $b;
} else {
  $a_b_ab = $y * 2 * $c + ceil(($x - $y) / 2) * $a;
}

#say join("\n", $naive, $all_ab, $a_b_ab, "----"); #debug

say min($naive, $all_ab, $a_b_ab);