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: Wrong Answer)

use std::*;

#[allow(dead_code)]
fn read<T: str::FromStr>() -> T {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|a| a.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2d<T: str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn main() {
    let v = read_vec::<u32>();
    let (a, b, c, mut x, mut y) = (v[0], v[1], v[2], v[3], v[4]);
    let mut sum = 0;

    if (a + b) >= 2 * c {
        let min = cmp::min(x, y);
        sum += c * 2 * min;
        if x < y {
            x = 0;
            y = y - x;
        } else {
            x = x - y;
            y = 0;
        }
    }
    sum += x * a + y * b;
    println!("{}", sum);
}