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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

$input = explode(' ', trim(fgets(STDIN)));
$k = (int)$input[0];
$a = (int)$input[1];
$b = (int)$input[2];

if ($b < 2 || $b <= $a + 2 || $a > $k-1 || $k <= 2) {
	echo $k + 1;
	exit();
}

$k -= ($a + 1);
$bis = $b;
if ($k > 1) {
	$exchange_count = floor($k / 2);
	$bis += (int)$exchange_count * ($b - $a);
}
if ($k % 2 === 1) {
	$bis += 1;
}
echo $bis;