
Score : 400 points
Problem StatementSnuke 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.
InputInput is given from Standard Input in the following format:
K A B
OutputPrint the maximum possible number of biscuits in Snuke's pocket after K operations.
Sample Input 14 2 6
Sample Output 17
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 27 3 4
Sample Output 28
Sample Input 3314159265 35897932 384626433
Sample Output 348518828981938099
