Problem:
Score : 400 points

Problem Statement

We have N points in a two-dimensional plane.

The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).

Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.

Here, points on the sides of the rectangle are considered to be in the interior.

Find the minimum possible area of such a rectangle.

Constraints

2 \leq K \leq N \leq 50

-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)

x_i≠x_j (1 \leq i<j \leq N)

y_i≠y_j (1 \leq i<j \leq N)

All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1
:
x_{N} y_{N}

Output

Print the minimum possible area of a rectangle that satisfies the condition.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var nk = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			int n = nk[0];
			int k = nk[1];
			var positions = new XY[n];
			for (int i = 0; i < n; i++) {
				var xy = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
				positions[i] = new XY { X = xy[0], Y = xy[1] };
			}

			long ans = long.MaxValue;
			for (int x = 0; x < n; x++) {
				for (int y = 0; y < n; y++) {
					for (int x2 = 0; x2 < n; x2++) {
						if (x == x2) {
							continue;
						}

						for (int y2 = 0; y2 < n; y2++) {
							if (y == y2) {
								continue;
							}

							
							long left = positions[x].X < positions[x2].X 
								? positions[x].X : positions[x2].X;
							long right = positions[x].X < positions[x2].X
								? positions[x2].X : positions[x].X;
							long bottom = positions[y].Y < positions[y2].Y
								? positions[y].Y : positions[y2].Y;
							long top = positions[y].Y < positions[y2].Y
								? positions[y2].Y : positions[y].Y;
							int count = 0;
							for (int i = 0; i < n; i++) {
								var pos = positions[i];
								if (pos.X >= left && pos.X <= right && pos.Y >= bottom && pos.Y <= top) {
									++count;
								}
							}

							if (count >= k) {
								long area = (right - left) * (top - bottom);
								ans = Math.Min(ans, area);
							}
						}
					}
				}
			}

			Console.WriteLine(ans);
		}

		public struct XY
		{
			public long X { get; set; }
			public long Y { get; set; }
		}
	}
}