Circum Triangle

Input

Contains at most $16$ test cases. Each test case begins with two integers $n (0 \leq n \leq 500)$ n~(0 \le n \le 500) and $r (0 < r \leq 100)$ r~(0 < r \le 100), where $n$ is the number of points and $r$ is the radius of the circle. The center of the circle is always at the origin.

The following $n$ lines each contain a real number $θ$ ( $0.0 \leq θ < 360.00$ 0.0 \le \theta < 360.00) — the angle in degrees between the corresponding point and the $x$ -axis. For example, if $θ = 30.00$ \theta = 30.00, then the coordinates of the point are

(r \cdot cos (30.0 0^{\circ}), r \cdot sin (30.0 0^{\circ}))

(r \cdot \cos(30.00^\circ),\ r \cdot \sin(30.00^\circ))

The last line contains $n = 0$ n = 0 and $r = 0$ r = 0 and should not be processed.

Output

For each test case, print one line — the sum of the areas of all possible triangles formed by the given $n$ points, rounded to the nearest integer.

Examples

Example 1

Loading