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 (1.15.1) (judge verdict: Accepted)

use std::io::BufRead;

pub struct StdinReader<R: BufRead> {
    pub buf_reader: R,
    pub buf: String,
}
impl<R: BufRead> StdinReader<R> {
    pub fn new(r: R) -> Self {
        StdinReader {
            buf_reader: r,
            buf: String::with_capacity(10000),
        }
    }
}

#[macro_export]
macro_rules! input {
    ($reader : expr, $t : ty) => { // one variable
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: $t = reader.buf.trim().parse().unwrap(); 
                reader.buf.clear();
                tmp_var
            },
        }
    };
    ($reader : expr, $t0 : ty, $t1 : ty) => { // 2 tuple
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: Vec<$t0> = reader.buf.trim().split_whitespace().map(|a| a.parse().unwrap()).collect();
                reader.buf.clear();
                (tmp_var[0].clone(), tmp_var[1].clone())
            }
        }
    };
    ($reader : expr, $t0 : ty, $t1 : ty, $t2 : ty) => { // 3 tuple
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: Vec<$t0> = reader.buf.trim().split_whitespace().map(|a| a.parse().unwrap()).collect();
                reader.buf.clear();
                (tmp_var[0].clone(), tmp_var[1].clone(), tmp_var[2].clone())
            }
        }
    };
    ($reader : expr, $t : ty; $size : expr) => { // Vector
        match &mut $reader {
            reader => {
                use std::io::BufRead;
                reader.buf_reader.read_line(&mut reader.buf).unwrap();
                let tmp_var: $t = reader.buf.trim().split_whitespace().map(|a| a.parse().unwrap()).collect();
                reader.buf.clear();
                tmp_var
            }
        }
    };
}

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

    let (k, a, b): (usize, usize, usize) = input!(r, usize, usize, usize);
    if a + 2 >= b || k - (a - 1) < 2 {
        println!("{}", k + 1);
    } else {
       let mut tmp = ((k - (a - 1)) / 2) * (b - a) + a;
       if (k - (a - 1)) % 2 == 1 {
           tmp += 1;
       }
       println!("{}", tmp);
    }
}