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 System.Numerics; 

class _Class
{
  void _Do()
  {
    var a = 0;
    var N = Split.ints();
    if (N[2]*2 < N[0] + N[1])
    {
      if (N[3] > N[4])
      {
        var a1 = N[4] * 2 * N[2];
        a1 += N[0] * (N[3] - N[4]);
        var a2 = N[3] * 2 * N[2];
        a = Math.Min(a1,a2);
      }
      else
      {
        var a1 = N[3] * 2 * N[2];
        a1 += N[1] * (N[4] - N[3]);
        var a2 = N[4] * 2 * N[2];
        a = Math.Min(a1, a2);
      }
        
    }
    else
    {
      a = N[0] * N[3] + N[1] * N[4];
    }
    
    //
    Console.WriteLine(a);
   }

  //
  static void Main(string[] args)
  {
    _(args);
    new _Class()._Do();
  }
  [Conditional("DEBUG")]
  static void _(string[] args)
  {
    if (args.Length != 0 && File.Exists(args[0]))
      Console.SetIn(new StreamReader(args[0]));
    else
      Console.Error.WriteLine("in");
  }
}

static class Split
{


  // 1
  public static string[] strings()
  {
    return Console.ReadLine().Split();
  }


  // [2.1] -2,147,483,648 ~ +2,147,483,647
  public static int[] ints()
  {
    var _s = Console.ReadLine().Split();

    var x = new int[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = int.Parse(_s[i]);

    return x;
  }

  // [2.2] 
  // -9,223,372,036,854,775,808 ~ 
  // +9,223,372,036,854,775,807
  public static long[] longs()
  {
    var _s = Console.ReadLine().Split();

    var x = new long[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = long.Parse(_s[i]);

    return x;
  }

  public static double[] doubles()
  {
    var _s = Console.ReadLine().Split();

    var x = new double[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = double.Parse(_s[i]);

    return x;
  }

  public static BigInteger[] bigs()
  {
    var _s = Console.ReadLine().Split();

    var x = new BigInteger[_s.Length];
    for (var i = 0; i < _s.Length; i++)
      x[i] = BigInteger.Parse(_s[i]);

    return x;
  }
}