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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;
using System.IO;
using System.Diagnostics;

class Scanner
{
    private readonly char Separator = ' ';
    private int Index = 0;
    private string[] Line = new string[0];
    public string Next()
    {
        if (Index >= Line.Length)
        {
            Line = Console.ReadLine().Split(Separator);
            Index = 0;
        }
        var ret = Line[Index];
        Index++;
        return ret;
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    private long NextLong()
    {
        return long.Parse(Next());
    }
}

class Magatro
{
    private int N, K;
    private int[] X, Y;
    private void Scan()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        K = sc.NextInt();
        X = new int[N];
        Y = new int[N];
        for (int i = 0; i < N; i++)
        {
            X[i] = sc.NextInt() - 1;
            Y[i] = sc.NextInt() - 1;
        }
    }

    private long Ans(int i, int j, int k, int l)
    {
        int MaxX = Math.Max(X[i], Math.Max(X[j], Math.Max(X[k], X[l])));
        int MinX = Math.Min(X[i], Math.Min(X[j], Math.Min(X[k], X[l])));
        int MaxY = Math.Max(Y[i], Math.Max(Y[j], Math.Max(Y[k], Y[l])));
        int MinY = Math.Min(Y[i], Math.Min(Y[j], Math.Min(Y[k], Y[l])));
        int cnt = 0;
        for (int n = 0; n < N; n++)
        {
            bool a = MinX <= X[n] && X[n] <= MaxX;
            bool b = MinY <= Y[n] && Y[n] <= MaxY;
            if (a && b)
            {
                cnt++;
            }
        }
        if (cnt >= K)
        {
            return (long)(MaxX - MinX) * (MaxY - MinY);
        }
        return long.MaxValue;
    }




    public void Solve()
    {
        Scan();

        long ans = long.MaxValue;
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            {
                for (int k = 0; k < N; k++)
                {
                    for (int l = 0; l < N; l++)
                    {
                        
                        ans = Math.Min(ans, Ans(i, j, k, l));
                    }
                }
            }
        }
        Console.WriteLine(ans);
    }

    static public void Main()
    {
        new Magatro().Solve();

    }
}