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 (3.8.2) (judge verdict: Time Limit Exceeded)

def main():
    a, b, c, x, y = map(int, input().split())

    min_sum = 100000 * 5000 + 100000 * 5000 + 200000 * 5000

    if a == c and b == c :
        min_sum = a * x + b * y
    elif a  < c and b < c  :
        min_sum = a * x + b * y
    elif a  > c and b  > c  :
        if x >= y :
            min_sum = y * 2 * c
            if a > c * 2:
                min_sum = min_sum + (x - y) * c * 2
            else:
                min_sum = min_sum + (x - y ) * a
        else:
            min_sum = x * 2 * c
            if b > c * 2:
                min_sum = min_sum + (y - x) * c * 2
            else:
                min_sum = min_sum + (y - x ) * b
    else:
        for i in range(0, x+1):
            for j in range(0, y+1):
                if min_sum > a * i + b * j + max(x-i, y-j) * c * 2:
                    min_sum =a * i + b * j + max(x-i, y-j) * c * 2

    print(min_sum)
main()