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.InputStreamReader;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Parser parser = new Parser();

        int A = parser.parseInt();
        int B = parser.parseInt();
        int C = parser.parseInt();
        int X = parser.parseInt();
        int Y = parser.parseInt();

        int minVal = Math.min(X, Y);
        System.out.println(minVal * Math.min(A + B, 2 * C) + (X - minVal) * Math.min(A, 2 * C) + (Y - minVal) * Math.min(B, 2 * C));
    }
}

class Parser {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final Iterator<String> stringIterator = br.lines().iterator();
    private static final Deque<String> inputs = new ArrayDeque<>();

    void fill() throws NoSuchElementException {
        if(inputs.isEmpty()){
            if(!stringIterator.hasNext()) throw new NoSuchElementException();
            inputs.addAll(Arrays.asList(stringIterator.next().split(" ")));
        }
    }

    Integer parseInt() throws NoSuchElementException {
        fill();
        if(!inputs.isEmpty()) {
            return Integer.parseInt(inputs.pollFirst());
        }
        throw new NoSuchElementException();
    }

    Double parseDouble() throws NoSuchElementException {
        fill();
        if(!inputs.isEmpty()) {
            return Double.parseDouble(inputs.pollFirst());
        }
        throw new NoSuchElementException();
    }

    String parseString() {
        fill();
        String string = inputs.pollFirst();
        if(string == null){
            throw new NoSuchElementException();
        }
        return string;
    }

}