Problem:
Score : 400 points

Problem Statement

Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.
He will perform the following operations exactly K times in total, in the order he likes:

Hit his pocket, which magically increases the number of biscuits by one.

Exchange A biscuits to 1 yen.

Exchange 1 yen to B biscuits.

Find the maximum possible number of biscuits in Snuke's pocket after K operations.

Constraints

1 \leq K,A,B \leq 10^9

K,A and B are integers.

Input

Input is given from Standard Input in the following format:

K A B

Output

Print the maximum possible number of biscuits in Snuke's pocket after K operations.

Sample Input 1

4 2 6

Sample Output 1

7

The number of biscuits in Snuke's pocket after K operations is maximized as follows:

Hit his pocket. Now he has 2 biscuits and 0 yen.

Exchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.

Hit his pocket. Now he has 1 biscuits and 1 yen.

Exchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.

Sample Input 2

7 3 4

Sample Output 2

8

Sample Input 3

314159265 35897932 384626433

Sample Output 3

48518828981938099

Solution in Rust (1.42.0) (judge verdict: Accepted)

use whiteread::parse_line;

fn main() {
    let (mut k, a, b): (usize, usize, usize) = parse_line().unwrap();
    let mut bis = 1;
    let mut yen = false;

    if a + 1 < b {
        while k > 1 {
            if yen {
                bis += b;
                yen = false;
            } else if bis < a {
                bis += 1;
            } else {
                bis -= a;
                yen = true;
            }
            k -= 1;
        }
        if yen {
            bis += b;
        } else {
            bis += 1;
        }
    } else {
        bis += k;
    }
    println!("{}", bis);
}