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: Wrong Answer)

using System;
namespace inonoa{
    class Ino{
        static void Main(){
            string[] input = Console.ReadLine().Split();
            int a = int.Parse(input[0]);
            int b = int.Parse(input[1]);
            int c = int.Parse(input[2]);
            int x = int.Parse(input[3]);
            int y = int.Parse(input[4]);

            int ans = 0;

            if(a>c){
                if(b>c){
                    if(x>y){
                        ans += y*2*c;
                        x -= y;
                        y = 0;
                        ans += Math.Min(2*x*c,x*a);
                        Console.WriteLine(ans);
                        return;
                    }else{
                        ans += x*2*c;
                        y -= x;
                        x = 0;
                        ans += Math.Min(2*y*c,x*b);
                        Console.WriteLine(ans);
                        return;
                    }
                }else if((a+b)/2.0f>=c){
                    if(x>y){
                        ans += y*2*c;
                        x -= y;
                        y = 0;
                        if(a>2*c){
                            ans += x*2*c;
                            Console.WriteLine(ans);
                            return;
                        }else{
                            ans += x*a;
                            Console.WriteLine(ans);
                            return;
                        }
                    }else{
                        ans += x*2*c;
                        y -= x;
                        x = 0;
                        if(b>2*c){
                            ans += x*2*c;
                            Console.WriteLine(ans);
                            return;
                        }else{
                            ans += y*b;
                            Console.WriteLine(ans);
                            return;
                        }
                    }
                }else{
                    ans += a*x + b*y;
                    Console.WriteLine(ans);
                    return;
                }
            }else{
                if(b>c){
                    if((a+b)/2.0f>=c){
                        if(y>x){
                            ans += x*2*c;
                            y -= x;
                            x = 0;
                            if(b>2*c){
                                ans += y*2*c;
                                Console.WriteLine(ans);
                                return;
                            }else{
                                ans += x*a;
                                Console.WriteLine(ans);
                                return;
                            }
                        }else{
                            ans += x*2*c;
                            y -= x;
                            x = 0;
                            if(b>2*c){
                                ans += x*2*c;
                                Console.WriteLine(ans);
                                return;
                            }else{
                                ans += x*a;
                                Console.WriteLine(ans);
                                return;
                            }
                        }
                    }else{
                        ans += a*x + b*y;
                        Console.WriteLine(ans);
                        return;
                    }
                }else{
                    ans += a*x + b*y;
                    Console.WriteLine(ans);
                    return;
                }
            }
        }
    }
}