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.Scanner;

class Main {
	int a,b,c;
	int x,y;

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		Main m = new Main(sc);
		m.solve();
		sc.close();
	}
	Main(Scanner sc){
		a = sc.nextInt();
		b = sc.nextInt();
		c = sc.nextInt();
		x = sc.nextInt();
		y = sc.nextInt();
	}
	void solve(){
		int cost = 0;
		if(a + b > 2 * c){
			while(x > 0 && y > 0){
				cost += 2 * c;
				x--;y--;
			}
			if(x > 0){
				if(a > 2 * c){
					while(x > 0){
						cost += 2 * c;
						x--;
					}
				} else {
					while(x > 0){
						cost += a;
						x--;
					}
				}
			} else if(y>0) {
				if(b > 2 * c){
					while(y > 0){
						cost += 2 * c;
						y--;
					}
				} else {
					while(y > 0){
						cost += b;
						y--;
					}
				}
			}
		} else {
			cost += a * x;
			x = 0;
			cost += b * y;
			y = 0;
		}
		System.out.println(cost);
	}
}