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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;
using static AtCoderTemplate.MyLibrary;

namespace AtCoderTemplate
{
    class Program
    {
        static void Main (string[] args)
        {
            string[] str;
            str = Console.ReadLine ().Split (' ');

            int A = int.Parse (str[0]);
            int B = int.Parse (str[1]);
            int C = int.Parse (str[2]);
            int X = int.Parse (str[3]);
            int Y = int.Parse (str[4]);

            long ans = 10000000000;
            long cost = 0;
            for (int i = (Max (X, Y)) * 2; i >= 0; i -= 2)
            {
                cost = A * Max (0, X - i / 2) + B * Max (0, Y - i / 2) + C * i;
                ans = Min (ans, cost);
            }

            Console.WriteLine (ans);
        }
    }

    class MyLibrary
    {
        public static int GCD (int a, int b)
        {
            if (a % b == 0) return b;
            return GCD (b, a % b);
        }
    }
}