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 (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.io.PrintWriter
import kotlin.concurrent.timerTask
import kotlin.math.max
import kotlin.math.min

val br = BufferedReader(InputStreamReader(System.`in`))
val out = PrintWriter(System.out)

fun main() {
    br.use { out.use {
        solve()
        out.flush()
    } }
}

fun solve() {
    val (a, b, c, x, y) = readLongList()
    var ans = Long.MAX_VALUE
    for (cTmp in 0..max(x * 2, y * 2)) {
        val tmp = cTmp / 2
        val atmp =  max(x - tmp, 0)
        val btmp =  max(y - tmp, 0)
        ans = min(ans, c * cTmp + a * atmp + b * btmp)
    }
    out.println(ans)
}

fun readInteger() = Integer.parseInt(br.readLine())
fun readLong() = java.lang.Long.parseLong(br.readLine())
fun readStringList() = br.readLine()!!.split(' ')
fun readIntegerList() = readStringList().map(Integer::parseInt)
fun readLongList() = readStringList().map(java.lang.Long::parseLong)
fun readDoubleList() = readStringList().map(java.lang.Double::parseDouble)