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: Wrong Answer)

import java.util.*;

public class Main{
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int A = sc.nextInt();
    int B = sc.nextInt();
    int C = sc.nextInt();
    int x = sc.nextInt();
    int y = sc.nextInt();
    int[][] dp = new int[x+1][y+1];
    for(int i=0; i<x+1; i++){
      for(int j=0; j<y+1;j++){
        if(i==0&&j==0) dp[i][j] = 0;
        else dp[i][j] = 1000007;
      }
    }

    for(int i=0; i<x+1; i++){
      for(int j=0; j<y+1; j++){
        if(i+1<x+1)dp[i+1][j] = Math.min(dp[i+1][j],dp[i][j] + A);
        if(j+1<y+1)dp[i][j+1] = Math.min(dp[i][j+1],dp[i][j] + B);
        if(i+1<x+1&&j+1<y+1) dp[i+1][j+1] = Math.min(dp[i+1][j+1],dp[i][j]+ 2*C);
      }
    }
    System.out.println(dp[x][y]);
  }
}