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 (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};
use std::cmp::{max, min};
#[allow(unused_mut)]
#[fastout]
fn main() {
    input! {
        a: usize,
        b: usize,
        c: usize,
        x: usize,
        y: usize
    }
    let a_b_min = if x < y { (a, x) } else { (b, y) };
    let a_b_max = if x > y { (a, x) } else { (b, y) };
    let all_ab = c * max(x, y) * 2;
    let sub_ab = c * a_b_min.1 * 2 + (a_b_max.1 - a_b_min.1) * a_b_max.0;
    let all_a_b = a * x + b * y;
    let res = min(all_ab, min(sub_ab, all_a_b));
    println!("{}", res);
}