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: Memory Limit Exceeded)

import java.util.*;
import java.util.stream.*;
import java.io.*;
import static java.util.Arrays.*;
import static java.lang.Math.*;

public class Main {

	static final Scanner in = new Scanner(System.in);
	static final PrintWriter out = new PrintWriter(System.out,false);

	static void solve() {
		int a = in.nextInt();
		int b = in.nextInt();
		int c = in.nextInt();
		int x = in.nextInt();
		int y = in.nextInt();
		int[][] dp = new int[x+1][y+1];
		for (int i=0; i<=x; i++) {
			Arrays.fill(dp[i], Integer.MAX_VALUE/2);
		}
		dp[0][0] = 0;
		for (int i=0; i<=x; i++) {
			for (int j=0; j<=y; j++) {
				if (dp[i][j] == Integer.MAX_VALUE/2) continue;
				if (i < x)
					dp[i+1][j] = Math.min(dp[i+1][j], dp[i][j] + a);
				if (j < y)
					dp[i][j+1] = Math.min(dp[i][j+1], dp[i][j] + b);
				if (i < x && j < y)
					dp[i+1][j+1] = Math.min(dp[i+1][j+1], dp[i][j] + 2*c);
			}
		}
		// trace(dp);
		out.println(dp[x][y]);
	}

	public static void main(String[] args) {
		long start = System.currentTimeMillis();

		solve();
		out.flush();

		long end = System.currentTimeMillis();
		//trace(end-start + "ms");
		in.close();
		out.close();
	}

	static void trace(Object... o) { System.out.println(Arrays.deepToString(o));}
}