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;
using System.Collections.Generic;
using System.Dynamic;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Reflection.Emit;
using System.Runtime.Remoting.Proxies;
using System.Text;
using static System.Console;
using static System.Math;
using static Ex;
class AC {
    /*------------------------------------------------------------------*/
    int A, B, C, X, Y;
    void Solve() {
        io.i(out A, out B, out C, out X, out Y);
        C *= 2;

        var ans = long.MaxValue / 2;
        REPEQ(Max(X, Y), i => ans = Min(ans,A*Max(0,X-i)+B*Max(0,Y-i)+C*i));

        io.o(ans);
    }
    /*------------------------------------------------------------------*/
    void Test() {
        //--- TEST ---//
    }
    public static void Main(string[] args) => new AC().Stream();
    IO io = new IO();
    private void Stream() {
        /*
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        SetIn(exStdIn);
        Test();
        */
        Solve();
        io.Flush();
    }
}
class IO {
    #region INPUT
    private const int Size = 1 << 12;
    private readonly Stream _stream = OpenStandardInput();
    private readonly byte[] _buffer = new byte[Size];
    private int _ptr = 0, _buffLen = 0;
    private bool HasNextByte() {
        if (_ptr < _buffLen)
            return true;
        _ptr = 0;
        _buffLen = _stream.Read(_buffer, 0, Size);
        return _buffLen > 0;
    }
    private byte ReadByte() {
        if (HasNextByte())
            return _buffer[_ptr++];
        else
            //inputの末尾の改行がないとerror
            throw new EndOfStreamException();

    }
    private bool IsAscii(int c) => '!' <= c && c <= '~';
    private char NextChar() {
        byte b = 0;
        do
            b = ReadByte(); while (!IsAscii(b));
        return (char)b;
    }
    private string Next() {
        var sb = new StringBuilder();
        for (var b = NextChar(); IsAscii(b); b = (char)ReadByte())
            sb.Append(b);
        return sb.ToString();
    }
    private void Read<T>(out T v) => v = SuitType<T>(Next());
    private bool TypeEqual<T, TU>() => typeof(T) == typeof(TU);
    private T SuitType<T>(string s) {
        if (TypeEqual<T, int>())
            ConvertType<T, int>(int.Parse(s));
        if (TypeEqual<T, long>())
            ConvertType<T, long>(long.Parse(s));
        if (TypeEqual<T, double>())
            ConvertType<T, double>(double.Parse(s));
        if (TypeEqual<T, char>())
            ConvertType<T, char>(char.Parse(s));
        return ConvertType<T, string>(s);
    }
    private T i<T>() => SuitType<T>(String);
    public string String => Next();
    public char Char => NextChar();
    public int Int => int.Parse(Next());
    public long Long => long.Parse(Next());
    public double Double => double.Parse(Next());
    public void i<T>(out T v) => Read(out v);
    public void i<T, TU>(out T t, out TU u) {
        i(out t);
        i(out u);
    }
    public void i<T, TU, TV>(out T t, out TU u, out TV v) {
        i(out t, out u);
        i(out v);
    }
    public void i<T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w) {
        i(out t, out u);
        i(out v, out w);
    }
    public void i<T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x) {
        i(out t, out u, out v);
        i(out w, out x);
    }
    public void i<T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y) {
        i(out t, out u, out v);
        i(out w, out x, out y);
    }
    public void ini<T>(out T[] a, int n) {
        a = new T[n];
        for (int i = 0; i < n; ++i)
            a[i] = i<T>();
    }
    public void ini<T, TU>(out T[] a, out TU[] b, int n) {
        a = new T[n];
        b = new TU[n];
        for (int i = 0; i < n; ++i) {
            a[i] = i<T>();
            b[i] = i<TU>();
        }
    }
    public void ini<T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n) {
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        for (int i = 0; i < n; ++i) {
            a[i] = i<T>();
            b[i] = i<TU>();
            c[i] = i<TV>();
        }
    }
    public void ini<T>(out T[,] a, int h, int w) {
        a = new T[h, w];
        for (int i = 0; i < h; ++i)
            for (int j = 0; j < w; ++j)
                a[i, j] = i<T>();
    }
    #endregion
    #region OUTPUT
    private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput()) {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public void Flush() => Console.Out.Flush();
    public void o(params Object[] xs) => Print(false, xs);
    public void o_(params Object[] xs) => Print(true, xs);
    private void Print(bool isOneLine, params Object[] xs) {
        foreach (var x in xs) {
            if (x is int[])
                PrintArr<int>(isOneLine, x);
            else if (x is long[])
                PrintArr<int>(isOneLine, x);
            else if (x is double[])
                PrintArr<int>(isOneLine, x);
            else if (x is char[])
                PrintArr<int>(isOneLine, x);
            else if (x is string[])
                PrintArr<int>(isOneLine, x);
            else if (x is bool[])
                PrintArr<int>(isOneLine, x);
            else if (x is int[,])
                PrintArr2D(ConvertType<int[,], object>(x));
            else if (x is long[,])
                PrintArr2D(ConvertType<long[,], object>(x));
            else if (x is double[,])
                PrintArr2D(ConvertType<double[,], object>(x));
            else if (x is char[,])
                PrintArr2D(ConvertType<char[,], object>(x));
            else if (x is string[,])
                PrintArr2D(ConvertType<string[,], object>(x));
            else if (x is bool[,])
                PrintArr2D(ConvertType<bool[,], object>(x));
            else
                WriteLine(x);
        }
    }
    private void PrintArr2D<T>(T[,] a) {
        int a0 = a.GetLength(0), a1 = a.GetLength(1);
        for (int i = 0; i < a0; ++i) {
            for (int j = 0; j < a1 - 1; ++j)
                Write(a[i, j] + " ");
            WriteLine(a[i, a1 - 1]);
        }
    }
    private void PrintArr<T>(bool isOneLine, Object xs) {
        if (isOneLine)
            PrintArr1D_(ConvertType<T[], object>(xs));
        else
            PrintArr1D(ConvertType<T[], object>(xs));
    }
    private void PrintArr1D<T>(T[] xs) {
        foreach (var x in xs)
            WriteLine(x);
    }
    private void PrintArr1D_<T>(T[] xs) => WriteLine(string.Join(" ", xs));
    public void YN(bool f) => WriteLine(f ? "YES" : "NO");
    public void Yn(bool f) => WriteLine(f ? "Yes" : "No");
    public void yn(bool f) => WriteLine(f ? "yes" : "no");
    #endregion
    private T ConvertType<T, TU>(TU v) => (T)Convert.ChangeType(v, typeof(T));
    public IO() { SetOut(_sw); }
}
static class Ex {
    public static void REP(int a, Action<int> act) => FOR(0, a, act);
    public static void FOR(int a, int b, Action<int> act) => FOR(a, b, 1, act);
    public static void FOR(int a, int b, int n, Action<int> act) {
        for (int i = a; i < b; i += n)
            act(i);
    }
    public static void REPEQ(int a, Action<int> act) => FOR(0, a + 1, act);
    public static void FOREQ(int a, int b, Action<int> act) => FOR(a, b + 1, act);
    public static void FOREQ(int a, int b, int n, Action<int> act) => FOR(a, b + 1, n, act);
    public static T MIN<T>(params T[] a) => a.Min();
    public static T MAX<T>(params T[] a) => a.Max();
}
static class NumEx {
    public static string toString(this double d) => d.ToString("R");
    public static string Pad0<T>(this T s, int n) => s.ToString().PadLeft(n, '0');
    public static int RoundOff(this double v, int n)
        => (int)Math.Round(v, n - 1, MidpointRounding.AwayFromZero);
    public static int RoundUp(this double v) => (int)Math.Ceiling(v);
    public static int RoundDown(this double v) => (int)Math.Floor(v);
    public static bool Odd(this int v) => (v & 1) != 0;
    public static bool Odd(this long v) => (v & 1) != 0;
}