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)

#![allow(unused)]

use std::{cmp, collections, fmt, io, iter, ops, str};
use cmp::Ordering::{Equal, Greater, Less};
use collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};
use io::{Read, Write};

#[cfg(feature = "debug")]
macro_rules! debug {
    ($fmt: expr) => { eprintln!($fmt) };
    ($fmt: expr, $($arg: tt)*) => { eprintln!($fmt, $($arg)*) };
}

#[cfg(not(feature = "debug"))]
macro_rules! debug {
    ($fmt: expr) => {};
    ($fmt: expr, $($arg: tt)*) => {};
}

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_owned()
}

fn read_word() -> String {
    const CAPACITY: usize = 16;

    let mut stdin = io::stdin();
    let mut byte: [u8; 1] = [0];

    loop {
        let mut buf = Vec::with_capacity(CAPACITY);

        loop {
            let res = stdin.read(&mut byte);

            if res.unwrap_or(0) == 0 || byte[0] <= b' ' {
                break;
            } else {
                buf.push(byte[0]);
            }
        }

        if buf.len() > 0 {
            return String::from_utf8(buf).unwrap();
        }
    }
}

fn parse_line<T: str::FromStr>() -> T {
    read_line().parse().ok().unwrap()
}

fn parse_word<T: str::FromStr>() -> T {
    read_word().parse().ok().unwrap()
}

fn parse_vec<T: str::FromStr>() -> Vec<T> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn flush() {
    io::stdout().flush();
}

fn main() {
    let a_price = parse_word::<i32>();
    let b_price = parse_word::<i32>();
    let ab_price = parse_word::<i32>();

    let calc_price = |a, b, ab| a as i32 * a_price + b as i32 * b_price + ab as i32 * ab_price;

    let a_num = parse_word::<usize>();
    let b_num = parse_word::<usize>();

    let mut a_buy = a_num;
    let mut b_buy = b_num;
    let mut ab_buy = 0;
    let mut price = calc_price(a_buy, b_buy, ab_buy);

    loop {
        debug!(
            "a: {}, b: {}, ab: {}, price: {}",
            a_buy,
            b_buy,
            ab_buy,
            calc_price(a_buy, b_buy, ab_buy)
        );

        if a_buy == 0 && b_buy == 0 {
            break;
        }

        let new_a_buy = a_buy - if a_buy > 0 { 1 } else { 0 };
        let new_b_buy = b_buy - if b_buy > 0 { 1 } else { 0 };
        let new_ab_buy = ab_buy + 2;

        let new_price = calc_price(new_a_buy, new_b_buy, new_ab_buy);
        if new_price > price {
            break;
        }

        a_buy = new_a_buy;
        b_buy = new_b_buy;
        ab_buy = new_ab_buy;
        price = new_price;
    }

    println!("{}", calc_price(a_buy, b_buy, ab_buy));
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test() {
        //
    }
}