Problem Background

After graduation, students are enthusiastically discussing their plans for high school. Everyone inevitably talks about the academic proficiency test.

In Zhejiang, high school students must not only take the National College Entrance Examination (commonly known as the "Gaokao") but also the General High School Academic Proficiency Test (referred to as the "Xuekao"). Students are required to take the Xuekao three times: in the second semester of their first year, the first semester of their second year, and the second semester of their second year.

Problem Description

Note: Some descriptions in the problem may differ from reality.

The Xuekao assesses all subjects in high school and grades the results in tiers from A to E, with A being the highest and E the lowest. Each subject determines the number of students in the E tier based on a fixed ratio $w$ (the same for all subjects). If a student receives an E grade (unqualified) in more than one subject, they will not be able to graduate.

In an alternate universe, there are $a$ subjects in total in high school. There are $b$ candidates across the province. If the cutoff for the E tier is set too high, it may result in some students being unable to graduate. Now, the head of the examination board has approached you to determine the maximum proportion of candidates that can be in the E tier (i.e., maximize the value of $w$) such that there exists at least one scenario where all candidates in Zhejiang can graduate.

If the number of candidates in the E tier calculated by a certain ratio is not an integer, round the number upwards.

Input and Output Formats

Input Format

A single line containing two positive integers $a$ and $b$.

Output Format

Output a floating-point number representing the maximum proportion of the E tier.

This problem uses a custom validator, and any result with an absolute error within $10^{-6}$ from the standard answer is considered correct.

Sample Input and Output

Sample Input #1

2 2

Sample Output #1

0.5000000000000000

Sample Input #2

114 514

Sample Output #2

0.0077821011673152

Sample Input #3

191 9810

Sample Output #3

0.0051987767584098

Notes

Sample 1 Explanation

Setting the E tier ratio to $\frac{1}{2}$, each subject has exactly one unqualified candidate. When the first candidate fails in the first subject and the second candidate fails in the second subject, all candidates can graduate. Therefore, $\frac{1}{2}$ is a valid solution.

It can be proven that no better solution exists.

Data Range and Constraints

For all data, $1 \leq a, b \leq 10000$.

$$ \def\arraystretch{1.5} \begin{array}{|c|c|}\hline \bf{Test Point} & \bf{Special Property} \\ \hline 1\sim3 & b=1\\\hline 4\sim6 & a=b \\\hline 7\sim10 & /\\\hline \end{array} $$

After solving this problem, can you explain why, in reality, the E tier in Zhejiang cannot exceed $5\%$?

见题面 Input 部分

见题面 Output 部分