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 Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::{max, min};
use std::i32;

fn solve(a: i32, b: i32, c: i32, x: i32, y: i32) -> i32 {
    let mut ans = i32::MAX;
    for nc in 0..(max(2 * x, 2 * y) + 1) {
        let na = max(0, x - nc / 2);
        let nb = max(0, y - nc / 2);
        let price = a * na + b * nb + c * nc;
        ans = min(ans, price);
    }
    ans
}

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    let mut iter = s.split_whitespace().map(|w| w.trim().parse().ok().unwrap());
    let a = iter.next().unwrap();
    let b = iter.next().unwrap();
    let c = iter.next().unwrap();
    let x = iter.next().unwrap();
    let y = iter.next().unwrap();
    let r = solve(a, b, c, x, y);
    println!("{}", r);
}