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::error::Error;
use std::io::{self, BufRead};

fn main() {
    run().unwrap()
}

fn run() -> Result<(), Box<Error>> {
    let stdin = io::stdin();
    let mut stdin = stdin.lock().lines();
    let (a, b, c, x, y) = {
        let line = stdin.next().unwrap()?;
        let mut it = line.split_whitespace().map(|s| s.parse::<u32>());
        (
            it.next().unwrap()?,
            it.next().unwrap()?,
            it.next().unwrap()?,
            it.next().unwrap()?,
            it.next().unwrap()?,
        )
    };

    if 2*c >= a + b {
        println!("{}", x*a + y*b);
    } else {
        if x > y {
            if 2*c*(x-y) > (x-y)*a {
                println!("{}", y*(2*c) + (x-y)*a);
            } else {
                println!("{}", x*2*c);
            }
        } else {
            if 2*c*(y-x) > (y-x)*b {
                println!("{}", x*(2*c) + (y-x)*b);
            } else {
                println!("{}", y*2*c);
            }
        }
    }

    Ok(())
}