Half and Half
"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.
- 1 ≤ A, B, C ≤ 5000
- 1 ≤ X, Y ≤ 105
- All values in input are integers.
Input is given from Standard Input in the following format:
A B C X Y
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
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
It is optimal to directly buy three A-pizzas and two B-pizzas.
Sample Input 3
1500 2000 500 90000 100000
Sample Output 3
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.