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};

fn main() {
    let stdin = std::io::stdin();
    let mut locked = stdin.lock();
    let mut sc = scanner::Scanner::new(&mut locked);

    let a = sc.next_signed();
    let b = sc.next_signed();
    let c = sc.next_signed();
    let x = sc.next_signed();
    let y = sc.next_signed();

    let r = (0..max(x, y) + 1)
        .map(|s| max(0, x - s) * a + max(0, y - s) * b + s * 2 * c)
        .min()
        .unwrap();

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

mod scanner {
    use std::io::{BufRead, Error, ErrorKind, Read};
    use std::str::FromStr;

    pub struct Scanner<'a, R>
    where
        R: 'a + BufRead + ?Sized,
    {
        reader: &'a mut R,
    }

    impl<'a, R> Scanner<'a, R>
    where
        R: 'a + BufRead + ?Sized,
    {
        pub fn new(reader: &'a mut R) -> Self {
            Scanner { reader: reader }
        }

        #[allow(dead_code)]
        pub fn next_byte(&mut self) -> u8 {
            self.reader
                .bytes()
                .skip_while(|ref c| !Self::is_printable(*c.as_ref().ok().unwrap()))
                .next()
                .unwrap()
                .unwrap()
        }

        #[allow(dead_code)]
        pub fn next_bytes(&mut self) -> Vec<u8> {
            self.reader
                .bytes()
                .skip_while(|ref c| !Self::is_printable(*c.as_ref().ok().unwrap()))
                .take_while(|ref c| Self::is_printable(*c.as_ref().ok().unwrap()))
                .collect::<Result<Vec<u8>, _>>()
                .unwrap()
        }

        #[allow(dead_code)]
        pub fn next_unsigned(&mut self) -> u64 {
            self.reader
                .bytes()
                .skip_while(|ref c| !Self::is_printable(*c.as_ref().ok().unwrap()))
                .take_while(|ref c| Self::is_printable(*c.as_ref().ok().unwrap()))
                .fold(Ok(0), |s, x| {
                    s.and_then(|t| {
                        x.and_then(|y| {
                            if b'0' <= y && y <= b'9' {
                                Ok(t * 10 + (y - b'0') as u64)
                            } else {
                                Err(Error::new(ErrorKind::InvalidData, "found not a digit"))
                            }
                        })
                    })
                })
                .unwrap()
        }

        #[allow(dead_code)]
        pub fn next_signed(&mut self) -> i64 {
            self.reader
                .bytes()
                .skip_while(|ref c| !Self::is_printable(*c.as_ref().ok().unwrap()))
                .take_while(|ref c| Self::is_printable(*c.as_ref().ok().unwrap()))
                .fold(Ok([0i64, 0]), |s, x| {
                    x.and_then(|y| {
                        s.and_then(|t| {
                            if t[0] == 0 && y == b'-' {
                                Ok([-1, 0])
                            } else if b'0' <= y && y <= b'9' {
                                Ok([
                                    if t[0] == 0 { 1 } else { t[0] },
                                    t[1] * 10 + (y - b'0') as i64,
                                ])
                            } else {
                                Err(Error::new(ErrorKind::InvalidData, "found not a digit"))
                            }
                        })
                    })
                })
                .and_then(|s| Ok(s[0] * s[1]))
                .unwrap()
        }

        #[allow(dead_code)]
        pub fn next_float(&mut self) -> f64 {
            self.reader
                .bytes()
                .skip_while(|ref c| !Self::is_printable(*c.as_ref().ok().unwrap()))
                .take_while(|ref c| Self::is_printable(*c.as_ref().ok().unwrap()))
                .collect::<Result<Vec<u8>, Error>>()
                .and_then(|t| {
                    String::from_utf8(t).or(Err(Error::new(ErrorKind::InvalidData, "invalid data")))
                })
                .and_then(|s| {
                    f64::from_str(&s).or(Err(Error::new(ErrorKind::InvalidData, "invalid data")))
                })
                .unwrap()
        }

        fn is_printable(c: u8) -> bool {
            0x21 <= c && c <= 0x7e
        }
    }
}