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 Perl (v5.18.2) (judge verdict: Wrong Answer)

while(<STDIN>){
	chomp;
    @line = split(/ /, $_);
    $K = $line[0];
    $A = $line[1]; # Aビスケット -> 1円
    $B = $line[2]; # Bビスケット <- 1円
}

if ($B - $A <= 2) {
	$Ans = $K+1;
} else {
	if ($K - $A < 2) {
		$Ans = $K+1;
    } else {
    	if (($K+1 - $A)%2 == 0) {
        	$Ans = ($B - $A) * ($K+1 - $A)/2 + $A
        } else {
        	$Ans = ($B - $A) * int(($K+1 - $A)/2) + $A + 1
        }
    }
}
#print "48518828981938099\n";
print "$Ans\n";