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 Python (3.4.3) (judge verdict: Accepted)

A, B, C, X, Y = map(int, input().split())

AB = A + B

num_A = 0
num_B = 0
num_C = 0
ans_cost = 5000 * 2 * 10**5
if 2 * C > AB:
    num_A = X
    num_B = Y
    num_C = 0
    ans_cost = int(A*num_A + B*num_B + C*num_C)
else:
    min_C = min(X,Y) *2
    max_C = max(X,Y) *2
    for i in range(min_C, max_C+1, 2):
        num_A = X - i / 2
        num_B = Y - i / 2
        if num_A < 1:
            num_A = 0
        if num_B < 1:
            num_B = 0
        
        total_cost = int(A*num_A + B*num_B + C*i)
    
        if total_cost < ans_cost:
            ans_cost = total_cost

print(ans_cost)