Score : $300$ points

问题陈述

Takahashi 拥有一颗等级为 $N$ 的红宝石。（他没有其他宝石。）
Takahashi 可以任意多次进行以下操作。

• 将一颗等级为 $n$（$n$ 至少为 $2$）的红宝石转换为“一颗等级为 $(n-1)$ 的红宝石和 $X$ 颗等级为 $n$ 的蓝宝石”。
• 将一颗等级为 $n$（$n$ 至少为 $2$）的蓝宝石转换为“一颗等级为 $(n-1)$ 的红宝石和 $Y$ 颗等级为 $(n-1)$ 的蓝宝石”。

Takahashi 希望获得尽可能多的等级为 $1$ 的蓝宝石。通过这些操作，他最多可以获得多少颗等级为 $1$ 的蓝宝石？

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

2 3 4

Sample Output 1

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 $12$.

Sample Input 2

1 5 5

Sample Output 2

0

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

Sample Input 3

10 5 5

Sample Output 3

3942349900

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

update @ 2024/3/10 11:01:19