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 Ruby (2.3.3) (judge verdict: Wrong Answer)

def ascan; gets.split.map(&:to_i);end

a,b,c,x,y = ascan

a1 = [a,c*2].min
a2 = [a*2,c*4].min
b1 = [b,c*2].min
b2 = [b*2,c*4].min
a1b1 = [a1+b1,c*2].min
a2b2 = [a2+b2,c*4].min

ans = 0

z = [x,y].min/2*2

ans += z/2*a2b2

x -= z
y -= z


if x >= 1 && y >= 1
    ans += [x/2*a2+(x%2)*a1+y/2*b2+(y%2)*b1, x/2*a2+y/2*b2+a1b1, [x,y].max/2*a2b2+a1b1].min
else
    ans += x/2*a2+(x%2)*a1+y/2*b2+(y%2)*b1
end

p ans