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 static System.Console;
using static System.Convert;

class Program
{
    static void Main(string[] args)
    {
        var input = Array.ConvertAll(ReadLine().Split(' '), ulong.Parse);
        var priceA = input[0];
        var priceB = input[1];
        var priceAB = input[2];
        var num1 = input[3];
        var num2 = input[4];
        var min = Math.Min(num1, num2);
        var maxPrice = min == num1 ? priceB : priceA;
        ulong result = 0;
        if (priceA + priceB >= 2 * priceAB) {
            if (maxPrice<=2*priceAB) result += 2 * priceAB * min;
            else { WriteLine(2 * priceAB * Math.Max(num1, num2));return; }
        }
        else { WriteLine(priceA * num1 + priceB * num2); return; }
        WriteLine((Math.Max(num1,num2) - min) * maxPrice+result);
    }
}