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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
namespace AtCoder.ARC096
{
    public class ARC096A
    {
        public static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int priceA = int.Parse(input[0]);
            int priceB = int.Parse(input[1]);
            int priceC = int.Parse(input[2]);
            int requiredA = int.Parse(input[3]);
            int requiredB = int.Parse(input[4]);

            int max = Math.Max(requiredA, requiredB);
            int min = GetPrice(priceA, priceB, priceC, requiredA, requiredB, 0);
            int price = 0;
            int numA = 0, numB = 0;
            for (int numC = 0; numC <= max * 2; numC += 2)
            {
                numA = Math.Max(requiredA - numC / 2, 0);
                numB = Math.Max(requiredB - numC / 2, 0);
                price = GetPrice(priceA, priceB, priceC, numA, numB, numC);
                if (price < min)
                {
                    min = price;
                }
            }
            Console.WriteLine(min);
        }

        private static int GetPrice(int priceA, int priceB, int priceC, int numA, int numB, int numC)
        {
            return priceA * numA + priceB * numB + priceC * numC;
        }
    }
}