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 PHP (7.4.4) (judge verdict: Accepted)

<?php
    list($A,$B,$C,$X_sum,$Y_sum)  = array_map('intval',explode(" ",trim(fgets(STDIN))));
    // echo $A,$B,$C,$X,$Y;
    //Cピザを$2k枚買うとすると
    // $X = $X_sum - 2*$k;
    // $Y = $Y_sum - 2*$k;
    $kingaku = INF;
 
    //合計金額は
    for($k=0;$k<=max($X_sum,$Y_sum);$k++){
        if(($Xk = $X_sum - $k)<0){
            $Xk = 0;
        }
        if(($Yk = $Y_sum - $k)<0){
            $Yk = 0;
        }
        $new_kingaku = ($A * ($Xk)) + ($B * ($Yk)) + $C * (2*$k);
        // echo $new_kingaku."\n";
        if($new_kingaku <= $kingaku){
            $sk = $k; 
            $kingaku = $new_kingaku;
        }
    }
    
    echo $kingaku."\n";
?>