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 test
{
    class Program
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            int A = line[0], B = line[1], C = line[2], X = line[3], Y = line[4], ans = 0;

            if (A + B <= 2 * C)
            {
                ans = A * X + B * Y;
                Console.WriteLine(ans);
                return;
            }

            int many = 0, few = 0, manyP = 0, fewP = 0;

            if (X >= Y)
            {
                many = X;
                few = Y;
                manyP = A;
                fewP = B;
            }
            else
            {
                many = Y;
                few = X;
                manyP = B;
                fewP = A;
            }
            
            ans += 2 * C * few;
            many -= few;
            few -= few;

            if (manyP > 2 * C)
            {
                ans += many * 2 * C;
            }else
            {
                ans += many * manyP;
            }            

            Console.WriteLine(ans);
        }
    }
}