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C - Changing Jewels

Score : $300$ points

Problem Statement

Takahashi has a red jewel of level $N$. (He has no other jewels.)
Takahashi can do the following operations any number of times.

• Convert a red jewel of level $n$ ($n$ is at least $2$) into "a red jewel of level $(n-1)$ and $X$ blue jewels of level $n$".
• Convert a blue jewel of level $n$ ($n$ is at least $2$) into "a red jewel of level $(n-1)$ and $Y$ blue jewels of level $(n-1)$".

Takahashi wants as many blue jewels of level $1$ as possible. At most, how many blue jewels of level $1$ can he obtain by the operations?

Constraints

• $1 \leq N \leq 10$
• $1 \leq X \leq 5$
• $1 \leq Y \leq 5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$ $Y$

Output

Print the answer.

2 3 4

12

Takahashi can obtain $12$ blue jewels of level $1$ by the following conversions.

• First, he converts a red jewel of level $2$ into a red jewel of level $1$ and $3$ blue jewels of level $2$.
  • After this operation, Takahashi has $1$ red jewel of level $1$ and $3$ blue jewels of level $2$.
• Next, he repeats the following conversion $3$ times: converting a blue jewel of level $2$ into a red jewel of level $1$ and $4$ blue jewels of level $1$.
  • After these operations, Takahashi has $4$ red jewels of level $1$ and $12$ blue jewels of level $1$.
• He cannot perform a conversion anymore.

He cannot obtain more than $12$ blue jewels of level $1$, so the answer is $12$.

1 5 5

0

Takahashi may not be able to obtain a blue jewel of level $1$.

10 5 5

3942349900

Note that the answer may not fit into a $32$-bit integer type.