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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var (N, K) = Read2Longs();
            var points = new List<Point>();
            for (int i = 0; i < N; i++)
            {
                var (x, y) = Read2Longs();
                points.Add(new Point { X = x, Y = y });
            }

            points = points.OrderBy(x => x.X).ToList();
            var min = long.MaxValue;
            for (int i = 0; i < N - 1; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    // 点が明らかにK個以下なので
                    if (j - i + 1 < K) continue;

                    var ps = points.Skip(i).Take(j - i + 1).OrderBy(x => x.Y).ToList();
                    for (int ii = 0; ii < ps.Count - 1; ii++)
                    {
                        for (int jj = 0; jj < ps.Count; jj++)
                        {
                            // 点が明らかにK個以下なので
                            if (jj - ii + 1 < K) continue;
                            {
                                var ps2 = ps.Skip(ii).Take(jj - ii + 1).ToList();

                                var rec = Math.Abs(ps.Max(x => x.X) - ps.Min(x => x.X))
                                    * Math.Abs(ps.Max(x => x.Y) - ps.Min(x => x.Y));
                                min = Math.Min(min, rec);
                            }
                        }
                    }
                }
            }

            return min;
        }
        [DebuggerDisplay("{X},{Y}")]
        class Point
        {
            public long X { get; set; }
            public long Y { get; set; }
        }

        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
}