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;
using System.Text;
using System.Threading.Tasks;
using System.Windows;

namespace AtCoder
{
    static class Program
    {
        static void Main()
        {
            //ここから

            var vs = IO.ReadLineToLongList();
            var A = vs[0];
            var B = vs[1];
            var C = vs[2];
            var X = vs[3];
            var Y = vs[4];

            long min = long.MaxValue;

            for (var i = 0; i <= 100000; i++)
            {
                long sum = 0;
                sum += 2 * C * i;
                sum += A * Math.Max(0, X - i);
                sum += B * Math.Max(0, Y - i);

                min = Math.Min(min, sum);
            }
                    

            //ここまで

            Console.WriteLine(min);
            Console.ReadKey();
        }

    }

    static class Func
    {
        static public long mod = 1000000007;
        static public void Swap<T>(ref T a, ref T b) { T temp = a; a = b; b = temp; }
        static public long GCD(long a, long b) { return b != 0 ? GCD(b, a % b) : a; }
        static public long LCM(long a, long b) { return (long)a * b / GCD(a, b); }
        static public long Factorial(long a) { return a == 1 ? a : a * Factorial(a - 1); }


        public static double ToAngle(this double radian)
        {
            return (double)(radian * 180 / Math.PI);
        }

        public static double ToRadian(this double angle)
        {
            return (double)(angle * Math.PI / 180);
        }

        static public long Conbination(long n,long m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * Conbination(n - 1, m - 1) / m;
        }

        static public void Factoring(long num, ref long[] vs)
        {
            if (num == 1)
            {
                vs[1]++;
            }
            for (long i = 2; i < Math.Sqrt(num); i++)
            {
                if (num % i == 0)
                {
                    vs[i]++;
                    Factoring(num / i, ref vs);
                }
            }
            vs[1]++;
        }
    }

    static class IO
    {
        static public string ReadLineToString() { return Console.ReadLine(); }
        static public long ReadLineToLong() { return long.Parse(Console.ReadLine()); }
        static public List<string> ReadLineToStringList() { return Console.ReadLine().Split(' ').ToList(); }
        static public List<long> ReadLineToLongList() { return Console.ReadLine().Split(' ').Select(long.Parse).ToList(); }

        static public List<double> ReadLineToDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }

        static public void WriteStrings(object[] strings) { foreach (var o in strings) { Console.Write(o + " "); } }
    }
}