Bob and stages

The citizens of BubbleLand are celebrating their 10th anniversary so they decided to organize a big music festival. Bob got a task to invite N famous singers who would sing on the fest. He was too busy placing stages for their performances that he totally forgot to write the invitation e-mails on time, and unfortunately he only found K available singers. Now there are more stages than singers, leaving some of the stages empty. Bob would not like if citizens of BubbleLand noticed empty stages and found out that he was irresponsible.

Because of that he decided to choose exactly K stages that form a convex set, make large posters as edges of that convex set and hold festival inside. While those large posters will make it impossible for citizens to see empty stages outside Bob still needs to make sure they don’t see any of the empty stages inside that area.

Since lots of people are coming, he would like that the festival area is as large as possible. Help him calculate the maximum area that he could obtain respecting the conditions. If there is no such area, the festival cannot be organized and the answer is 0.00.

Input

The first line of input contains two integers N (3 ≤ N ≤ 200) and K (3 ≤ K ≤ min(N, 50)), separated with one empty space, representing number of stages and number of singers, respectively.

Each of the next N lines contains two integers X _i and Y _i (0 ≤ X _i, Y _i ≤ 10⁶) representing the coordinates of the stages. There are no three or more collinear stages.

Output

Output contains only one line with one number, rounded to exactly two decimal places: the maximal festival area. Rounding is performed so that 0.5 and more rounds up and everything else rounds down.

Example

input

5 4
0 0
3 0
2 1
4 4
1 5

output

10.00

Note

Example explanation: From all possible convex polygon with 4 vertices and no other vertex inside, the largest is one with points (0, 0), (2, 1), (4, 4) and (1, 5).

import java.util.*;
import java.io.*;

public class H {

class Point {
int x, y;
int id1, id2;

public Point(int x, int y) {
this.x = x;
this.y = y;
}

int q() {
if (x == 0 && y == 0) {
return 0;
} else if (x > 0 || (x == 0 && y > 0)) {
return 1;
} else {
return 2;
}
}
@Override
public String toString() {
return "Point [x=" + x + ", y=" + y + ", id1=" + id1 + ", id2=" + id2 + "]";
}
}

long vectMul(Point a, Point b) {
return 1L * a.x * b.y - 1L * a.y * b.x;
}

long vectMul(Point a, Point b, Point c) {
return 1L * (b.x - a.x) * (c.y - a.y) - 1L * (b.y - a.y) * (c.x - a.x);
}

void solve() {
int n = in.nextInt();
int k = in.nextInt();
Point[] a = new Point[n];
for (int i = 0; i < n; i++) {
			a[i] = new Point(in.nextInt(), in.nextInt());
		}
		Arrays.sort(a, (p1, p2) -> {
if (p1.x != p2.x) {
return p1.x - p2.x;
}
return p1.y - p2.y;
});

long result = 0;
long[][] dp = new long[n][k + 1];
long[][] cost = new long[n][n];
long INF = Long.MIN_VALUE / 3;
Point[] buf = new Point[n];
for (int i = 0; i < buf.length; i++) {
			buf[i] = new Point(0, 0);
		}
		Point[] vecs = new Point[n * (n - 1)];
		for (int i = 0, tmp = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				if (i != j) {
					vecs[tmp] = new Point(a[j].x - a[i].x, a[j].y - a[i].y);
					vecs[tmp].id1 = i;
					vecs[tmp].id2 = j;
					tmp++;
				}
			}
		}
		Arrays.sort(vecs, (p1, p2) -> {
int q1 = p1.q(), q2 = p2.q();
if (q1 != q2) {
return q1 - q2;
}
return -Long.signum(vectMul(p1, p2));
});
for (int start = 0; start < n; start++) {
			for (int i = n - 1; i >= start; i--) {
a[i].x -= a[start].x;
a[i].y -= a[start].y;
}
for (int i = 0; i < n; i++) {
				Arrays.fill(dp[i], INF);
				Arrays.fill(cost[i], INF);
			}
			dp[start][0] = 0;

			int size = 0;
			for (int i = start + 1; i < n; i++) {
				buf[size].x = a[i].x;
				buf[size].y = a[i].y;
				buf[size].id1 = i;
				size++;
			}
			Arrays.sort(buf, 0, size, (p1, p2) -> {
long v = vectMul(p1, p2);
return -Long.signum(v);
});

for (int i = 0; i < size; i++) {
				for (int j = i + 1; j < size; j++) {
					int p1 = buf[i].id1, p2 = buf[j].id1;
					boolean ok = true;
					for (int t = i + 1; t < j; t++) {
						if (vectMul(buf[i], buf[j], buf[t]) > 0) {
ok = false;
break;
}
}
if (ok) {
cost[p1][p2] = vectMul(buf[i], buf[j]);
}
}
}
for (int i = 0; i < size; i++) {
				cost[start][buf[i].id1] = cost[buf[i].id1][start] = 0;
			}

			for (Point vec : vecs) {
				int p1 = vec.id1, p2 = vec.id2;
				long cst = cost[p1][p2];
				if (cst != INF) {
					long[] dp1 = dp[p1], dp2 = dp[p2];
					for (int i = 0; i < k; i++) {
						dp2[i + 1] = Math.max(dp2[i + 1], dp1[i] + cst);
					}
				}
			}
			result = Math.max(result, dp[start][k]);
		}

		out.printf("%d.%02d\n", result / 2, 50 * (result % 2));
	}

	FastScanner in;
	PrintWriter out;

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public String nextToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextToken());
		}

		public long nextLong() {
			return Long.parseLong(nextToken());
		}

		public double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

	public static void main(String[] args) {
		new H().run();
	}
}