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: Wrong Answer)

use std::io;
use std::io::prelude::*;

fn main() {
    let mut stdin = io::stdin();
    let mut buf = String::new();
    let _ = stdin.read_to_string(&mut buf);
    let mut iter = buf.split_whitespace();
    let k: usize = iter.next().unwrap().parse().unwrap();
    let a: usize = iter.next().unwrap().parse().unwrap();
    let b: usize = iter.next().unwrap().parse().unwrap();

    let mut ans = 1;

    if b - a <= 1 || k - a + 1 <= 0{
        ans += k;
    } else {
        ans += a - 1;
        ans += (k - a + 1) / 2 * (b - a);
        if (k - a + 1) % 2 == 1 {
            ans += 1;
        }
    }

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