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: Wrong Answer)

using System;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;

namespace ForAtcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            long price = 10000000;
            long[] inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
            var a = inputLongArray[0];
            var b = inputLongArray[1];
            var c = inputLongArray[2];
            var x = inputLongArray[3];
            var y = inputLongArray[4];
            for (long i = 0; i <= x; i++)
            {
                for (long j = 0; j <= y; j++)
                {
                    long k = ( x - i >= y - j ? x - i : y - j);
                    if (price > a * i + b * j + 2 * c * k)
                    {
                        price = a * i + b * j + 2 * c * k;
                    }
                }
            }
            Console.WriteLine(price);
        }
    }
}