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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int A = sc. nextInt();
        int B = sc. nextInt();
        int C = sc. nextInt();
        
        int X = sc. nextInt();
        int Y = sc. nextInt();
        
        boolean Aflag = X > Y;
        
        int Z = 0;
        
        if (Aflag){ 
            Z = X - Math.abs(X-Y);
        }else{
            Z = Y - Math.abs(X-Y);
        }
        
        long price = 0;
        
        if ((A+B) > C*2){
            price += Z*C*2;
            if (Aflag){
                if (A < 2*C){
                    price += (X-Z)*A;
                }else{
                    price += (X-Z)*2*C;
                }
            }else{
                if (B < 2*C){
                    price += (Y-Z)*B;
                }else{
                    price += (Y-Z)*2*C;
                }
            }
            
        }else{
            price += A*X;
            price += B*Y;
        }
        
        System.out.println(price);
    }
}