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.IO;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Text;

partial class Solver {
    public void Run() {
        var A = ni();
        var B = ni();
        var AB = ni();
        var X = ni();
        var Y = ni();

        var ABcands = new[] { 0, X, Y };

        int ans = int.MaxValue;

        foreach (var abNum in ABcands) {
            var cost = abNum * AB * 2;
            cost += A * Math.Max(0, X - abNum);
            cost += B * Math.Max(0, Y - abNum);

            ans = Math.Min(ans, cost);
        }

        cout.WriteLine(ans);
    }
}

// PREWRITEN CODE BEGINS FROM HERE
partial class Solver : Scanner {
    public static void Main(string[] args) {
        new Solver(Console.In, Console.Out).Run();
    }

    TextReader cin;
    TextWriter cout;

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        this.cin = reader;
        this.cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

    public int ni() { return NextInt(); }
    public int[] ni(int n) { return NextIntArray(n); }
    public long nl() { return NextLong(); }
    public long[] nl(int n) { return NextLongArray(n); }
    public double nd() { return NextDouble(); }
    public string ns() { return Next(); }
}

public class Scanner {
    private TextReader Reader;
    private Queue<String> TokenQueue = new Queue<string>();
    private CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        this.Reader = reader;
    }

    public int NextInt() { return Int32.Parse(Next(), ci); }
    public long NextLong() { return Int64.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        var array = new string[size];
        for (int i = 0; i < size; i++) array[i] = Next();
        return array;
    }
    public int[] NextIntArray(int size) {
        var array = new int[size];
        for (int i = 0; i < size; i++) array[i] = NextInt();
        return array;
    }

    public long[] NextLongArray(int size) {
        var array = new long[size];
        for (int i = 0; i < size; i++) array[i] = NextLong();
        return array;
    }

    public String Next() {
        if (TokenQueue.Count == 0) {
            if (!StockTokens()) throw new InvalidOperationException();
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext() {
        if (TokenQueue.Count > 0)
            return true;
        return StockTokens();
    }

    private bool StockTokens() {
        while (true) {
            var line = Reader.ReadLine();
            if (line == null) return false;
            var tokens = line.Trim().Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) continue;
            foreach (var token in tokens)
                TokenQueue.Enqueue(token);
            return true;
        }
    }
}