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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel.DataAnnotations;
using System.Diagnostics.CodeAnalysis;
using System.Linq;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Math;

class Program
{
    static void Main()
    {
        var (A, B, C, X, Y) = ReadLine().Split(' ').Select(int.Parse).ToArray();

        var ans = Range(0, Max(X, Y) + 1).Select(i => A * Max(X - i, 0) + B * Max(Y - i, 0) + C * (i * 2)).Min();

        WriteLine(ans);
    }
}

static class ArrayDeconstructExtensions
{
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2) => (i1, i2) = (a[0], a[1]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3) => (i1, i2, i3) = (a[0], a[1], a[2]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4) => (i1, i2, i3, i4) = (a[0], a[1], a[2], a[3]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4, out T i5) => (i1, i2, i3, i4, i5) = (a[0], a[1], a[2], a[3], a[4]);
}