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: Wrong Answer)

# -*- coding: utf-8 -*-
"""
Created on Tue Mar 31 11:58:49 2020

@author: black
"""


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


a_num = X
b_num = Y
c_num = 0
total = A*a_num + B*b_num + C*c_num

ans = 10**10
P_MAX = max(A,B)
P_MIN = min(A, B)
MAX = max(X, Y)
MIN = min(X, Y)

if 2*C >= 2*P_MAX:
    ans = total
elif 2*P_MAX > 2*C and 2*C > A + B:
    for i in range(MIN, MAX+1):
        a_num = X-i
        b_num = Y-i
        c_num = 2*i
        T = A*a_num + B*b_num + C*c_num
        total = min(total, T)
elif A + B >= 2*C and 2*C > 2*P_MIN:
    c_num = MIN*2
    if A>B:
        a_num = 0
        b_num = Y-MIN
        total = A*a_num + B*b_num + C*c_num
    else:
        a_num = X-MIN
        b_num = 0
        total = A*a_num + B*b_num + C*c_num
else:
    a_num = 0
    b_num = 0
    c_num = MAX*2
    total = A*a_num + B*b_num + C*c_num
ans = total
print(ans)