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No.379 Five-Yen Coin

レベル : / AI推定難易度 : 101 / 実行時間制限 : 1ケース 1.000秒 / メモリ制限 : 256 MB / 小数誤差許容問題　絶対誤差または相対誤差が $10^{-12}$ 以下。ただし、ジャッジ側の都合で500桁未満にしてください
タグ : （AC するまで非表示） / 解いたユーザー数 468
作問者 : LayCurse
お気に入りにしたユーザー ProblemId : 898 / 自分の提出
問題文最終更新日: 2023-08-15 01:47:56
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Problem Statement

You are contemplating suicide by gas.
Each time you insert $1$ five-yen coin, $G \; \mathrm{mg}$ of gas comes out.
You currently have $N$ yen and can exchange money freely.
The volume of your room is $V \; \mathrm{m}^3$.
For simplicity, assuming that no gas leaks out of the room, at most how many $\mathrm{mg}$ of gas per $1 \; \mathrm{m^3}$ can you fill the room with?

Input

$N$ $G$ $V$

$1 \leq N, G, V \leq 1000000000 = 10^9$
$N, G, V$ are integers

Output

Output a real number representing the answer.
Your answer is considered correct if its relative error or absolute error is at most $10^{-12}$.

Sample

Sample 1
Input
100 500 10
Output
1000

Since you have $100$ yen, you can obtain $5$-yen coins, $20$ of them.
Also, each $5$-yen coin, per $1$ coin, releases $500 \; \mathrm{mg}$ of gas, so a total of $10000 \; \mathrm{mg}$ of gas can be released.
The volume of the room is $10 \; \mathrm{m}^3$, so the concentration is $1000 \; \mathrm{mg}/\mathrm{m}^3$.

Sample 2
Input
187456612 84877661 9498174
Output
335030261.51740765571594238281

You may output any number of digits (within reason), but note that the relative error or absolute error must be at most $10^{-12}$.

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