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::str::FromStr;
use std::io::stdin;

fn main() {
    let (a, b, c, x, y) = {
        let vec: Vec<i64> = read_vec();
        (vec[0], vec[1], vec[2], vec[3], vec[4])
    };
    let mut amount = (a * x) + (b * y);
    let mut min = amount;
    let mut a_count = x;
    let mut b_count = y;
    for _ in 0..(x + y) {
        amount += 2 * c;
        if a_count > 0 {
            amount -= a;
            a_count -= 1;
        }
        if b_count > 0 {
            amount -= b;
            b_count -= 1;
        }
        min = std::cmp::min(min, amount);
    }
    println!("{}", min);
}

fn read_vec<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).err();
    line.trim().split_whitespace().
        map(|x| x.parse().ok().unwrap()).collect()
}