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.Linq;
using System.Collections.Generic;
using System.IO;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {

            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }

        public static long d(long sx,long sy,long gx,long gy)
        {
            return Math.Abs(gx - sx) + Math.Abs(gy - sy);
        }
      



        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var abcxy = Reads();
            if (abcxy[0] + abcxy[1] > 2 * abcxy[2])
            {
                if (abcxy[0] <= 2 * abcxy[2] && abcxy[1] <= 2 * abcxy[2])
                {
                    if (abcxy[3] > abcxy[4])
                        Console.WriteLine(2 * abcxy[2] * abcxy[4] + (abcxy[3] - abcxy[4]) * abcxy[0]);
                    else
                        Console.WriteLine(2 * abcxy[2] * abcxy[3] + (abcxy[4] - abcxy[3]) * abcxy[1]);
                }
                else if (abcxy[0] >= 2 * abcxy[2] && abcxy[1] <= 2 * abcxy[2])
                {
                    if (abcxy[3] > abcxy[4])
                        Console.WriteLine(2 * abcxy[2] * abcxy[3]);
                    else
                        Console.WriteLine(2 * abcxy[2] * abcxy[3] + (abcxy[4] - abcxy[3]) * abcxy[1]);
                }
                else if(abcxy[0] <= 2 * abcxy[2] && abcxy[1] >= 2 * abcxy[2])
                {
                    if (abcxy[3] > abcxy[4])
                        Console.WriteLine(2 * abcxy[2] * abcxy[4]+ (abcxy[3] - abcxy[4]) * abcxy[0]);
                    else
                        Console.WriteLine(2 * abcxy[2] * abcxy[4]);
                }
                else if(abcxy[0] >= 2 * abcxy[2] && abcxy[1] >= 2 * abcxy[2])
                {
                    Console.WriteLine(2 * abcxy[2] * Math.Max(abcxy[3], abcxy[4]));
                }
            }
            else
            {
                Console.WriteLine(abcxy[0] * abcxy[3] + abcxy[1] * abcxy[4]);
            }
             

            Console.Out.Flush();
        }
    }
}