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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("1500 2000 1600 3 2");
            //7900
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("1500 2000 1900 3 2");
            //8500
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("1500 2000 500 90000 100000");
            //100000000
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] wkArr = InputList[0].Split(' ').Select(pX => int.Parse(pX)).ToArray();

        int A = wkArr[0];
        int B = wkArr[1];
        int C = wkArr[2];
        int X = wkArr[3];
        int Y = wkArr[4];

        int Answer = int.MaxValue;
        for (int LoopAB = 0; LoopAB <= Math.Max(X, Y) * 2; LoopAB++) {
            int Cost = LoopAB * C;

            int RestA = X - LoopAB / 2;
            int RestB = Y - LoopAB / 2;

            RestA = Math.Max(RestA, 0);
            RestB = Math.Max(RestB, 0);

            Cost += RestA * A;
            Cost += RestB * B;

            if (Answer > Cost)
                Answer = Cost;
        }
        Console.WriteLine(Answer);
    }
}