D. Delicious Pizza
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Dima has several brothers and one pizza. The pizza is a circle with a radius of $$$1$$$. Dima wants to share the pizza fairly, ensuring that:

  • each slice has a "crust" (a segment with a non-zero arc length),
  • the area of the smallest slice is maximized.

On the circumference of the pizza, there are $$$N$$$ olives positioned at different angles. The task is to cut the pizza into exactly $$$K$$$ slices using $$$K - 1$$$ straight cuts. Each cut must pass through two olives, and every cut, except for the first, must start where the previous cut ended.

Input

The first line contains two integers $$$N$$$ and $$$K$$$ ($$$2 \leq N \leq 30$$$, $$$2 \leq K \leq N$$$) — the number of olives and the number of slices the pizza needs to be cut into. The second line contains $$$N$$$ distinct integers $$$P_i$$$ ($$$0 \leq P_i \leq 359$$$) — the polar angles in degrees that define the positions of the $$$i$$$-th olive. All $$$P_i$$$ are unique and sorted in ascending order. The center of the polar coordinate system is the center of the pizza.

Output

Output the area of the smallest slice of pizza when optimally cut. The answer must have an absolute or relative error not exceeding $$$10^{-5}$$$.

Examples
Input
3 2
0 60 270
Output
1.05899694
Input
4 4
85 90 265 270
Output
0.08721110