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;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main{

	public static void main(String[] args) throws IOException {
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter wr = new PrintWriter(System.out);
        String str = br.readLine().trim();
        StringTokenizer stk = new StringTokenizer(str);
        int A = Integer.parseInt(stk.nextToken());
        int B = Integer.parseInt(stk.nextToken());
        int C = Integer.parseInt(stk.nextToken());
        int X = Integer.parseInt(stk.nextToken());
        int Y = Integer.parseInt(stk.nextToken());
        long first=0l,second=0l,third = 0l;
        first = (long)A*X+B*Y;
        //System.out.println(Math.min(A, B)+Math.min(C,D));
        if(X>Y) {
        	int left = X-Y;
        	second = (long)Y*2*C;second+=left*A;
        }
        else {
        	int left = Y-X;
        	second = (long)X*2*C;second+=left*B;
        }
        if(X>Y)third = (long)(X+X)*C;
        else third = (long)(Y+Y)*C;
        System.out.println(Math.min(first, Math.min(second, third)));
	}

}