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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;
typedef long long LL;
int main(int argc, char* argv[])
{
	LL A,B,C,X,Y;
	cin>>A>>B>>C>>X>>Y;

	if (A*X+B*Y<C*max(X,Y)){
		cout<<A*X+B*Y<<endl;
		return 0;
	}
	if (2*C>=A+B){
		cout<<A*X+B*Y<<endl;
		return 0;
	}
	LL c=2*C*max(X,Y);
	LL d=A*X+B*Y;
	if (X==Y){
		cout<<min(min(2*X*C,c),d)<<endl;
	}else if (X>Y){
		cout<<min(min(2*Y*C+A*(X-Y),c),d)<<endl;
	}else{
		cout<<min(min(2*X*C+A*(Y-X),c),d)<<endl;
	}
	return 0;
}