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)

#!/usr/bin/env python3
import sys


def solve(A: int, B: int, C: int, X: int, Y: int):
    # > なお、ピザの組み替えにより、必要な量を超えたピザが発生しても構いません。
    val_min = 5001 * (X+Y)
    for z in range(0, 2*max(X, Y)+1, 2):
        x = max(0, X - z//2)
        y = max(0, Y - z//2) 
        val_min_cond = A*x + B*y + C*z
        #print(x,y,z,val_min_cond)
        val_min = val_min_cond if val_min_cond < val_min else val_min
    print(val_min)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    A = int(next(tokens))  # type: int
    B = int(next(tokens))  # type: int
    C = int(next(tokens))  # type: int
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(A, B, C, X, Y)

if __name__ == '__main__':
    main()