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 C (GCC 9.2.1) (judge verdict: Accepted)

#include<stdio.h>

int min(int a, int b){return a < b ? a : b;}
int max(int a, int b){return a > b ? a : b;}

int main(void){
    int a, b, c, x, y;
    
    scanf("%d%d%d%d%d", &a, &b, &c, &x, &y);
    
    //ABピザを使わない場合
    int notAB_price = a * x + b * y;
 
    int all_AB = c * max(x, y) * 2;

    int withAB_price;

    withAB_price = c * min(x, y) * 2;//ABピザの値段
    if(x < y){                  
        withAB_price += (y - x) * b;//Bピザの必要枚数が多い場合は買い足す
    }else if(y < x){
        withAB_price += (x - y) * a;
    }
    int ans = min(withAB_price, min(notAB_price, all_AB));
    printf("%d", ans);

    return 0;
}
//この問題のポイント：long intを使う，
//long int を使う場合は，printf で %ldを使う
//max（） 関数を定義する