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.

4 2 6

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.

7 3 4

8

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