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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
ini_set('error_reporting', E_ALL & ~E_NOTICE);

// define('DEBUG', true);
define('DEBUG', false);

fscanf(STDIN, "%d %d %d %d %d", $A, $B, $C, $X, $Y);

$maxC = max($X, $Y) * 2;

$answer = PHP_INT_MAX;

for ($CC = 0; $CC <= $maxC; $CC += 2) {
	// Cピザを2枚買うとAピザを1枚買わなくて済む
	$AA = max(0, $X - $CC / 2);
	// Cピザを2枚買うとBピザを1枚買わなくて済む
	$BB = max(0, $Y - $CC / 2);
	$cost = $AA * $A + $BB * $B + $CC * $C;

	if (DEBUG) {
		printf("A:%d B:%d C:%d\n", $AA, $BB, $CC);
	}

	$answer = min($answer, $cost);
}
echo $answer;