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11097: 【原1097】Enclose



author: Guangda Huzhang 原OJ链接:


There are n circles in a plane with equal radius. Now we wanna draw a shortest enclosed curve, and every circles lie in this curve. You have to write a program to calculate the length of this curve.

Input Format

The input contains multiple testcases.

For each case, the first line contains two integer \(n\) and \(r\) \((1\leq n\leq 10000)\) denoting the number of circles and the radius of them. After that there are \(n\) lines, each line contains two integers denoting the coordinate of each circle.The absolute value of then would not be greater then 10000, and the radius is no large than 10000.

Output Format

For each case output one real number (round to 0.01) which is the length of that curve.

Sample Input

2 1
-1 0
1 0
5 1
1 0
0 1
-1 0
0 -1
0 0

Sample Output


Case Limits

Time limit: 500 msec

Memory limit: 64 MB

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