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 ConsoleApp6
{
    class Program
    {
        static void Main(string[] args)
        {
            var elements = Console.ReadLine().Split(' ');
            var a = int.Parse(elements[0]);
            var b = int.Parse(elements[1]);
            var c = int.Parse(elements[2]);
            var X = int.Parse(elements[3]);
            var Y = int.Parse(elements[4]);

            var min = -1;
            foreach(var aN in Enumerable.Range(0, X + 1))
            {
                var cN = (X - aN) * 2;
                var bN = Y - cN / 2;

                var sum = aN * a + cN * c;
                if (bN > 0) sum += bN * b;
                if (min < 0 || sum < min) min = sum;
            }

            foreach (var bN in Enumerable.Range(0, Y + 1))
            {
                var cN = (Y - bN) * 2;
                var aN = X - cN / 2;

                var sum = bN * b + cN * c;
                if (aN > 0) sum += aN * a;
                if (min < 0 || sum < min) min = sum;
            }
            Console.WriteLine(min);
        }
    }
}