2009 Bulgarian Olympiad in Informatics

There is a dangerous minefield somewhere in Bulgaria. You have been assigned to enclose them all with a "warning band" so that future travellers are aware of the danger.

After searching around with a metal detector, you have located all of the mines. Each mine is a perfectly round shape with radius $R$ at location $x$, $y$. Can you write a program to determine the length of the shortest band that will enclose all of the mines?

Input Specification

On the first line of the standard input, two integers $N$ and $R$ will be given - the number of the mines and their radius. On the next $N$ lines, the coordinates $x$ and $y$ of the center of a mine will be given. The mines will overlap (in order to create a more powerful blast, for example).

$N$ will be between $1$ and $10000$, inclusive, and $x$, $y$ will be between $-20000$ and $20000$.

Output Specification

Output a single line, containing the minimal length of a band.
Your answer will be considered correct if it is within $0.001$ of the answer.

Sample Input

8 1
1 4
3 2
7 9
5 4
9 5
6 7
9 1
11 8

Sample Output

34.408

Diagram