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