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## 문제

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.

## 입력

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

n r
x1 y1
.
.
.
xn yn

n is the number of vertices of the polygon (3 ≤ n ≤ 10). r is the radius of the disk (1 ≤ r ≤ 100). xi and yi give the coordinate values of the i-th vertex of the polygon (1 ≤ i ≤ n). Coordinate values satisfy 0 ≤ xi ≤ 100 and 0 ≤ yi ≤ 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°. Note that the border of a convex polygon never crosses or touches itself.

## 출력

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).

## 예제 입력 1

4 4
0 0
6 0
6 6
0 6


## 예제 출력 1

35.759506


## 예제 입력 2

3 1
0 0
2 1
1 3


## 예제 출력 2

2.113100


## 예제 입력 3

3 1
0 0
100 1
99 1


## 예제 출력 3

0.019798


## 예제 입력 4

4 1
0 0
100 10
100 12
0 1


## 예제 출력 4

3.137569


## 예제 입력 5

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


## 예제 출력 5

177.728187


## 예제 입력 6

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


## 예제 출력 6

7181.603297