# Cover the Polygon with Your Disk

Time Limit : 5 sec, Memory Limit : 262144 KB

## Problem J Cover the Polygon with Your Disk

A convex polygon is drawn on a flat paper sheet. You are trying to place a disk in your hands to cover as large area of the polygon as possible. In other words, the intersection area of the polygon and the disk should be maximized.

### Input

The input consists of a single test case, formatted as follows. All input items are integers.

$n$ $r$
$x_1$ $y_1$
.
.
.
$x_n$ $y_n$

$n$ is the number of vertices of the polygon ($3 \leq n \leq 10$). $r$ is the radius of the disk ($1 \leq r \leq 100$). $x_i$ and $y_i$ give the coordinate values of the $i$-th vertex of the polygon ($1 \leq i \leq n$). Coordinate values satisfy $0 \leq x_i \leq 100$ and $0 \leq y_i \leq 100$.

The vertices are given in counterclockwise order. As stated above, the given polygon is convex. In other words, interior angles at all of its vertices are less than 180$^{\circ}$. Note that the border of a convex polygon never crosses or touches itself.

### Output

Output the largest possible intersection area of the polygon and the disk. The answer should not have an error greater than 0.0001 ($10^{-4}$).

### Sample Input 1

4 4
0 0
6 0
6 6
0 6

### Sample Output 1

35.759506

### Sample Input 2

3 1
0 0
2 1
1 3

### Sample Output 2

2.113100

### Sample Input 3

3 1
0 0
100 1
99 1

### Sample Output 3

0.019798

### Sample Input 4

4 1
0 0
100 10
100 12
0 1

### Sample Output 4

3.137569

### Sample Input 5

10 10
0 0
10 0
20 1
30 3
40 6
50 10
60 15
70 21
80 28
90 36

### Sample Output 5

177.728187

### Sample Input 6

10 49
50 0
79 10
96 32
96 68
79 90
50 100
21 90
4 68
4 32
21 10

### Sample Output 6

7181.603297

Source: ACM International Collegiate Programming Contest , Asia Regional Tsukuba, Tsukuba, Japan, 2016-10-16
http://icpc.iisf.or.jp/2016-tsukuba/