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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

	static class Pizza {
		int num;
		int money;

		Pizza(int n, int m) {
			this.num = n;
			this.money = m;
		}

		int getnum() {
			return num;
		}

		int getmoney() {
			return money;
		}
	}

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		// A B C X Y
		int A = sc.nextInt();
		int B = sc.nextInt();
		int C = sc.nextInt();

		int X = sc.nextInt();
		int Y = sc.nextInt();

		int A_B = A + B;

		Pizza p_B;
		Pizza p_S;

		if (X > Y) {
			p_B = new Pizza(X, A);
			p_S = new Pizza(Y, B);
		} else {
			p_S = new Pizza(X, A);
			p_B = new Pizza(Y, B);
		}

		int ans = 0;
		if (A_B > C * 2) {
			ans = C * p_S.getnum() * 2;
		} else {
			ans = A_B * p_S.getnum();
		}

		int n = p_B.getnum() - p_S.getnum();

		if (p_B.getmoney() > C * 2) {
			ans = ans + n * C * 2;
		} else {
			ans = ans + n * p_B.getmoney();
		}

		System.out.println(ans);
		sc.close();

	}
}