#include <iostream>
#include <iomanip>
#include <fstream>
#include <cmath>

#define N_MAX (40)
#define M_MAX (40)
#define PI    (3.14159265358979324)

using namespace std;

double area(double p1, double p2, double p3)
{
	p1 *= 2.0 * PI;
	p2 *= 2.0 * PI;
	p3 *= 2.0 * PI;
	return (sin(p2 - p1) + sin(p3 - p2) + sin(p1 - p3)) / 2.0;
}

int main(void)
{
	ifstream cin("scope.txt");
	int n, m;
	while(cin >> n >> m) {
		if(n == 0 && m == 0) break;

		double p[N_MAX];
		double Smax[M_MAX][N_MAX][N_MAX];

		for(int i = 0; i < n; i++) {
			cin >> p[i];
		}

		for(int h = 0; h < m; h++) {
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < n; j++) {
					Smax[h][i][j] = 0.0;
				}
			}
		}

		double Sans;

		for(int h = 2; h < m; h++) {
			Sans = 0.0;
			for(int i = 0; i < n; i++) {
				for(int j = i + h; j < n; j++) {
					for(int k = i + h - 1; k < j; k++) {
						double S = area(p[i], p[k], p[j]) + Smax[h-1][i][k];
						Smax[h][i][j] = max(Smax[h][i][j], S);
						Sans = max(Sans, S);
					}
				}
			}
		}

		cout << setiosflags(ios::fixed) << setprecision(6)
			 << Sans << endl;
	}

	return 0;
}