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.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;

namespace AtcoderExpress
{


    class Program
    {

        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = NK[0];
            var K = NK[1];
            var points = new List<Tuple<long, long>>();
            for (int i = 0; i < N; i++)
            {
                var XY = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
                var X = XY[0];
                var Y = XY[1];
                points.Add(new Tuple<long, long>(X, Y));
            }

            //X座標でのソート
            points = points.OrderBy(tuple => tuple.Item1).ToList();
            var ans = long.MaxValue;
            //左端を1番目からN-1番目まで動かす
            for (int i = 0; i < N; i++)
            {
                //右端の範囲を設定
                for (int j = i; j < N; j++)
                {
                    var left = points[i];
                    var right = points[j];

                    long xmin = Min(left.Item1, right.Item1);
                    long xmax = Max(left.Item1, right.Item1);

                    //y座標の高さの決定
                    for (int m = i; m <= j; m++)
                    {
                        for (int n = m; n <= j; n++)
                        {
                            long ymin = Min(points[n].Item2, points[m].Item2);
                            long ymax = Max(points[n].Item2, points[m].Item2);
                            long rec = (xmax - xmin) * (ymax - ymin);
                            //y座標の範囲にK個以上座標があるかどうかの検索
                            var CumPoint = 0L;
                            for (int k = i; k <= j; k++)
                            {
                                if (points[k].Item2 <= ymax && points[k].Item2 >= ymin)
                                {
                                    CumPoint++;
                                }
                            }

                            if (CumPoint >= K && rec < ans)
                            {
                                ans = rec;
                            }
                        }
                    }

                }
            }
            Console.WriteLine(ans);
        }


    }
}