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 ABC096_C
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');

            int A = int.Parse(input[0]);  //それぞれのピザの金額
            int B = int.Parse(input[1]);
            int AB = int.Parse(input[2]);
            int needA = int.Parse(input[3]);  //ピザの必要枚数
            int needB = int.Parse(input[4]);

            int common = Math.Min(needA , needB); //AとBが両方存在しているとき
            int single = Math.Abs(needA - needB); //残りがAとBのどちらかのとき
            int moreNeed = needA > needB ? A : B; //要求数の多いほうを代入
            int total = Math.Min((A + B) * common, AB * common * 2) + Math.Min(moreNeed * single, AB * single * 2);
            Console.WriteLine(total);


            //if (AB <= A / 2 && AB <= B / 2)
            //{
            //    totalMin = AB * Math.Max(needA, needB) * 2;
            //}
            //else if (AB <= (Math.Abs(A - B) / 2 + Math.Min(A, B)))
            //{
            //    int defNeed = Math.Abs(needA - needB);
            //    if (needA < needB)
            //    {
            //        totalMin = B * defNeed + AB * needA * 2;
            //    }
            //    else if (needA > needB)
            //    {
            //        totalMin = A * defNeed + AB * needB * 2;
            //    }
            //    else
            //    {
            //        totalMin = AB * needA * 2;
            //    }
            //}
            ////else if (A < AB / 2 || B < AB / 2)
            ////{
            ////    totalMin = A * needA + B * needB;
            ////}
            //else if (AB > (Math.Abs(A - B) / 2 + Math.Min(A, B)))
            //{
            //    totalMin = A * needA + B * needB;
            //}
            //else
            //{
            //    totalMin = A * needA + B * needB;
            //}
            //Console.WriteLine(totalMin);
            //return;

            //for (int a = 0; a <= needA; a++)  //小文字のa,bはピザの枚数
            //{
            //    for (int b = 0; b <= needB; b++)
            //    {
            //        int ab = Math.Max(needA - a, needB - b) * 2;
            //        if (ab < 0)  //abは必ず2枚ずつでないとaとbの1枚ずつにカウントされない
            //        {
            //            ab = 0;
            //        }

            //        money = a * A + b * B + ab * AB;
            //        if (a == 0 && b == 0)
            //        {
            //            totalMin = money;
            //        }
            //        else if (a == needA && b == needB)
            //        {
            //            Console.WriteLine(Math.Min(totalMin, money));
            //            return;
            //        }
            //        else
            //        {
            //            totalMin = Math.Min(totalMin, money);
            //        }
            //    }
            //}
        }
    }
}