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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <math.h>

int max(int x, int y);


int main()
{
    int a, b, c;
    int x, y;
    int minSum;
    int maxNumberOfAb;

    scanf("%d %d %d %d %d", &a, &b, &c, &x, &y);

    maxNumberOfAb = max(x, y) * 2;
    minSum = a * x + b * y + c * (x + y); // dummy
    for (int i = 0; i <= maxNumberOfAb; i++)
    {
	int needA = x - (int)floor(i / 2);
	int needB = y - (int)floor(i / 2);

	if (needA < 0)
	{
	    needA = 0;
	}
	if (needB < 0)
	{
	    needB = 0;
	}
	
	int sum = a * needA + b * needB + c * i;

	if (sum < minSum)
	{
	    minSum = sum;
	}
    }

    printf("%d\n", minSum);
    
    return 0;
}

int max(int x, int y)
{
    if (x > y)
    {
	return x;
    }
    else
    {
	return y;
    }
}