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: Wrong Answer)

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

namespace ARC96
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            int a = int.Parse(s[0]);
            int b = int.Parse(s[1]);
            int c = int.Parse(s[2]);
            int x = int.Parse(s[3]);
            int y = int.Parse(s[4]);

            int min_ab = Math.Min(a, b);
            int max_ab = Math.Max(a, b);
            int min_xy = Math.Min(x, y);
            int max_xy = Math.Max(x, y);

            if (min_ab > c)
            {
                Console.WriteLine(2 * c * max_xy);
            }
            else if (max_ab > 2 * c && 2 * c > min_ab)
            {
                if (a >= b)
                {
                    if (x >= y)
                    {
                        Console.WriteLine(2 * c * (x - y) + b * y);
                    }
                    else
                    {
                        Console.WriteLine(2 * c * x + b * y);
                    }
                }
                else
                {
                    if (x <= y)
                    {
                        Console.WriteLine(2 * c * (y - x) + a * x);
                    }
                    else
                    {
                        Console.WriteLine(2 * c * y + a * x);
                    }
                }
            }
            else if (max_ab >= c && c >= min_ab)
            {
                long min_price = 5000000000;
                for (int i = 0; i < max_xy; i++)
                {
                    min_price = Math.Min(i * 2 * c + (min_xy - i) * min_ab, min_price);

                }
                Console.WriteLine(min_price);
            }

            else if (a + b >= 2 * c)
            {
                if (x > y)
                {
                    Console.WriteLine(2 * c * y + (x - y) * a);
                }
                else
                {
                    Console.WriteLine(2 * c * x + (y - x) * b);
                }
            }
            else
            {
                Console.WriteLine(a * x + b * y);
            }
        }
    }
}