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We have a special convex that all points have the same distance to origin point. 

As you know we can get N segments after linking the origin point and the points on the convex. We can also get N angles between each pair of the neighbor segments.  Now give you the data about the angle, please calculate the area of the convex 

Input

There are multiple test cases. 

The first line contains two integer N and D indicating the number of the points and their distance to origin. (3 <= N <= 10, 1 <= D <= 10)  The next lines contain N integers indicating the angles. The sum of the N numbers is always 360. 

Output

For each test case output one float numbers indicating the area of the convex. The printed values should have 3 digits after the decimal point. 

Sample Input

4 190 90 90 906 160 60 60 60 60 60

Sample Output

2.0002.598

 

 n边形的面积可以拆分成n个三角形面积之和

而已知每个三角形的两边及两边夹角，我们可以通过三角形面积公式算出每个三角形的面积，相加之和便是最终的n边形面积

无需考虑角度x大于180度情况 此情况下 按s=0.5*a*b*sinx计算 sinx为负值 减去该面积即可

 

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