/* Sat Oct 25 00:00:25 JST 2003 */
/* Sat Oct 25 00:56:01 JST 2003 */
#include <stdio.h>
#include <math.h>

int n, m;
double areatable[42][42];
double max;

double rec(double area, int cur, int len, int first)
{
  int i;
  double max = 0.0, tmp;

  if (len >= m) {
    return area + areatable[cur][first];
  }

  for (i = cur+1; i < n; i++) {
    if (max < (tmp = rec(area + areatable[cur][i], i, len+1, first))) max = tmp;
  }
  return max;
}

double maxarea(void)
{
  int i;
  double max = 0.0, tmp;

  for (i = 0; i < n; i++) {
    if (max < (tmp = rec(0, i, 1, i))) max = tmp;
  }
  return max;
}


int main()
{
  int i, j;
  double p[42];
  
  while (1) {
    scanf("%d %d", &n, &m);
    if (n == 0 && m == 0) break;

    for (i = 0; i < n; i++) {
      scanf("%lf", &p[i]);
    }

    for (i = 0; i < n; i++) {
      for (j = i; j < n; j++) {
	if (j == i) areatable[i][j] = 0;
	else {
	  areatable[i][j] = sin((p[j] - p[i]) * M_PI * 2) / 2;
	  areatable[j][i] = -areatable[i][j];
	}
      }
    }
    printf("%lf\n", maxarea());
  }

  return 0;
}