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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC095_C_2
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ');
            var A = double.Parse(input[0]);
            var B = double.Parse(input[1]);
            var AB = double.Parse(input[2]);
            var X = double.Parse(input[3]);
            var Y = double.Parse(input[4]);

            var commonCount = Math.Min(X, Y); //XとYの両方必要な分量
            var remainingCount = Math.Abs(X - Y);
            double ans = 0;
            if (AB <= (A + B) / 2)
            {
                ans += AB * commonCount*2;
                if (X > Y)
                {
                    if (AB*2 > A)
                    {
                        ans += A * remainingCount;
                    }
                    else
                    {
                        ans += AB * remainingCount*2;
                    }
                }
                else if (Y > X)
                {
                    if (AB*2 > B)
                    {
                        ans += B * remainingCount;
                    }
                    else
                    {
                        ans += AB * remainingCount*2;
                    }
                }
            }
            else
            {
                ans += A * X + B * Y;
            }

            Console.WriteLine(ans);
        }
    }
}