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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
        "fmt"
)

func solution(a, b, c, x, y int) int {
        if 2*c < a && 2*c < b {
                return max(x, y) * c * 2
        }

        if 2*c > a+b {
                return a*x + b*y
        }

        out := c * 2 * min(x, y)
        t := min(x, y)
        x -= t
        y -= t

        out += a*x + b*y
        return out
}

func min(x, y int) int {
        if x < y {
                return x
        }
        return y
}
func max(x, y int) int {
        if x > y {
                return x
        }
        return y
}

func main() {
        var a, b, c, x, y int
        fmt.Scan(&a, &b, &c, &x, &y)
        fmt.Println(solution(a, b, c, x, y))
}