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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>)
{
    val (a, b, c, x, y) = readNInts()

    val candidate = mutableListOf<Int>()
    for (i in 0..(listOf(x, y).max()!! * 2) step 2)
    {
        var tmp = x - i / 2
        val na = if (tmp > 0) tmp else 0
        tmp = y - i / 2
        val nb = if (tmp > 0) tmp else 0

        candidate.add(a * na + b * nb + c * i)
    }

    println(candidate.min())
}

// Read an integer
// Usage: val a = readInt()
fun readInt() = readLine()!!.toInt()

// Read N integers separated by " "
// Usage: val (a, b, c) = readNInts()
fun readNInts() = readLine()!!.split(" ").map(String::toInt)

// Read a string
// Usage: val a = readString()
fun readString() = readLine()!!