When I hit my pocket...

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.

Examples

Input

4 2 6

Output

7

Input

7 3 4

Output

8

Input

314159265 35897932 384626433

Output

48518828981938099

inputFormat

Input

Input is given from Standard Input in the following format:

K A B

outputFormat

Output

Print the maximum possible number of biscuits in Snuke's pocket after K operations.

Examples

Input

4 2 6

Output

7

Input

7 3 4

Output

8

Input

314159265 35897932 384626433

Output

48518828981938099

样例

4 2 6

7