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.Diagnostics;
using System.IO;
using System.Linq;
using static System.Math;

namespace Half_And_Half
{
    class Program
    {
        public static void Main(string[] args)
        {
            using (var sc = new SetConsole())
            {
                var input = GetArray<int>();
                int a = input[0], b = input[1], c = input[2], x = input[3], y = input[4];
                if (a + b <= 2 * c)
                {
                    CWrite(a * x + b * y);
                    return;
                }
                else
                {
                    int tmp = Min(x, y) * 2 * c;
                    int tmp2 = tmp + 2 * c * Abs(x - y);
                    int tmp3 = tmp + Abs(x - y) * (x > y ? a : b);
                    CWrite(Min(tmp2, tmp3));
                }
            }
        }

        static void CWrite<T>(T str) => Console.WriteLine(str);
        static string GetString() => Console.ReadLine();
        static T[] GetArray<T>()
        {
            var t = typeof(T);
            var str = Console.ReadLine();
            if (t == typeof(string))
            {
                return (T[])(object)str.Split();
            }
            if (t == typeof(int))
            {
                return (T[])(object)str.ToNumArray<T>();
            }
            if (t == typeof(long))
            {
                return (T[])(object)str.ToNumArray<T>();
            }
            if (t == typeof(double))
            {
                return (T[])(object)str.ToNumArray<T>();
            }
            throw new NotSupportedException($"{t} is not supported.");
        }
    }



    class SetConsole : IDisposable
    {
        readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
        public SetConsole()
        {
            sw.AutoFlush = false;
            Console.SetOut(sw);
        }
        public void Dispose()
        {
            Console.Out.Flush();
            sw.AutoFlush = true;
            Console.SetOut(sw);
        }
    }

    static class ExtentionsLibrary
    {
        public static T[] ToNumArray<T>(this string str)
        {
            var t = typeof(T);
            if (t == typeof(int))
            {
                return (T[])(object)str.Split().Select(int.Parse).ToArray();
            }
            if (t == typeof(long))
            {
                return (T[])(object)str.Split().Select(long.Parse).ToArray();
            }
            if (t == typeof(double))
            {
                return (T[])(object)str.Split().Select(double.Parse).ToArray();
            }
            throw new NotSupportedException();
        }

        public static int ToInt(this string str) => int.Parse(str);
    }
}