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;

class Exercise1
    {
        static int a = 0;
        static int b = 0;
        static int c = 0;
        static int xx = 0;
        static int yy = 0;
        static void Main()
        {
            String input = Console.ReadLine();
            try
            {
                a = Int32.Parse(input.Split(' ')[0]);
                b = Int32.Parse(input.Split(' ')[1]);
                c = Int32.Parse(input.Split(' ')[2]);
                xx = Int32.Parse(input.Split(' ')[3]);
                yy = Int32.Parse(input.Split(' ')[4]);
            }
            catch (Exception)
            {
                Console.ReadLine();
                return;
            }
            
            bool shouldAB = (a + b) > 2 * c;
            bool shouldBuyA = a < c * 2;
            bool shouldBuyB = b < c * 2;
            int result = 0;
            if (!shouldAB)
            {
                result = xx * a + yy * b;
            } else
            {
                if (xx > yy)
                {
                    result = 2 * c * yy;
                    if (shouldBuyA)
                    {
                        result += (xx - yy) * a;
                    } else
                    {
                        result += (xx - yy) * 2 * c;
                    }
                } else
                {
                    result = 2 * c * xx;
                    if (shouldBuyB)
                    {
                        result += (yy - xx) * b;
                    }
                    else
                    {
                        result += (yy - xx) * 2 * c;
                    }
                }
                
            }
            Console.WriteLine(result);
            Console.ReadLine();
        }
    }