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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) {
        try {
            // 標準入力
            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            String strArr[] = br.readLine().split(" ");
            int a = Integer.parseInt(strArr[0]);
            int b = Integer.parseInt(strArr[1]);
            int c = Integer.parseInt(strArr[2]);
            int x = Integer.parseInt(strArr[3]);
            int y = Integer.parseInt(strArr[4]);

            int ans1 = a * x + b * y;

            int ans2 = 0;
            int ans3 = 0;
            if (x > y) {
                ans2 += (c * 2) * y;
                ans3 += (c * 2) * y;
                ans2 += (x - y) * a;
                ans3 += (x - y) * (c * 2);
            } else {
                ans2 += (c * 2) * x;
                ans3 += (c * 2) * x;
                ans2 += (y - x) * b;
                ans3 += (y - x) * (c * 2);
            }

            if (ans1 > ans2) {
                if (ans2 > ans3) {
                    System.out.println(ans3);
                } else {
                    System.out.println(ans2);
                }
            } else {
                if (ans1 > ans3) {
                    System.out.println(ans3);
                } else {
                    System.out.println(ans1);
                }
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

}