Maximum Polygon
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## Algorithms, Convex Hull, Geometry, Searching algorithm, Ternary search

Problem
Editorial
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Given $N$ points on plane, the $N$ points forms a convex polygon. You need to find $M$ points among them, then we calculate the convex hull of the $M$ points.

You need to maximize $\frac{The\ area\ of\ the\ convex\ hull}{The\ perimeter\ of\ the\ convex\ hull}$.

## Input Format

First line contains two integers $N,M(2\le M\le N\le 120)$.

Each of the next $N$ lines contains two integers $X_i,Y_i(-10^9\le X_i,Y_i\le 10^9)$, represent a point.

It's guaranteed no two points coincide.

## Output Format

One float number, represent the answer, round to 4 decimal digits. It's guaranteed the output will not change if we add $10^{-6}$ to the answer or subtract $10^{-6}$ from the answer.

Note : The statement for this problem has been updated. We are rejudging all submissions, please check announcement on contest page for detailed issue.

SAMPLE INPUT
6 4
1 0
2 1
2 2
1 3
0 1
0 2

SAMPLE OUTPUT
0.4109

Explanation The sample is in the above graph. $Area=3,Perimeter\approx 7.300563$.

Time Limit: 5.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

## This Problem was Asked in

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