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;

namespace TestApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var str = Console.ReadLine()
                .Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries)
                .Select(_ => int.Parse(_))
                .ToArray();
            int a = str[0];
            int b = str[1];
            int c = str[2];
            int x = str[3];
            int y = str[4];
            var sum = int.MaxValue;
            var count = x + y;
            int i = 0;
            while (true)
            {
                var maxA = 0 < x - i ? x - i : 0;
                var maxB = 0 < y - i ? y - i : 0;
                var value = i * 2 * c + maxA*a + maxB*b;
                if (sum > value)
                    sum = value;
                if ((i / 2) > count)
                    break;
                i++;
            }
            Console.WriteLine(sum);

                //for (int i = 0; i <= count; i++)
                //{

            //    for (int j = 0; j <= count - i; j++)
            //    {

            //        var z = (count - i - j);
            //        var xx = (int)(i + z * 0.5);
            //        var yy = (int)(j + z * 0.5);
            //        if ((xx == x && yy == y) && sum > xx * a + yy * b + z * c)
            //        {
            //            sum = (i * a + j * b + z * c);
            //        }

            //    }
            //}
            //Console.WriteLine(sum);
            Console.ReadLine();


        }
        
    }

}