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::io::{Read, StdinLock};
use std::str::{from_utf8, FromStr};
use std::vec::Vec;

struct StdinReader<'a> {
    reader: StdinLock<'a>,
}

impl<'a> StdinReader<'a> {
    pub fn new(reader: StdinLock<'a>) -> StdinReader {
        StdinReader { reader: reader }
    }

    pub fn read<T: FromStr>(&mut self) -> T {
        fn is_whitespace(ch: u8) -> bool {
            ch == 0x20 || ch == 0x0a || ch == 0x0d
        }

        let token: Vec<u8> = self.reader
            .by_ref()
            .bytes()
            .map(|ch| ch.expect("failed to read a byte"))
            .skip_while(|ch| is_whitespace(*ch))
            .take_while(|ch| !is_whitespace(*ch))
            .collect();
        let token_str = from_utf8(&token)
            .unwrap_or_else(|_| panic!(format!("invalid utf8 sequence: {:?}", token)));
        token_str
            .parse()
            .unwrap_or_else(|_| panic!(format!("failed to parse input: {}", token_str)))
    }
}

fn main() {
    let stdin = std::io::stdin();
    let mut reader = StdinReader::new(stdin.lock());

    let a: i64 = reader.read();
    let b: i64 = reader.read();
    let c: i64 = reader.read();
    let x: i64 = reader.read();
    let y: i64 = reader.read();

    let mut min_cost = std::i64::MAX;

    for k in 0..(x + y + 1) {
        // ABピザを 2*k 個買う
        let i = max(x - k, 0);
        let j = max(y - k, 0);
        let cost = i * a + j * b + 2 * k * c;
        min_cost = min(min_cost, cost);
    }

    println!("{}", min_cost);
}