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: Wrong Answer)

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

namespace Program
{
    public class ABC075D
    {
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static int NextInt() => int.Parse(NextString());
            public static long NextLong() => long.Parse(NextString());
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static public void Main(string[] args)
        {
            var N = Console_.NextInt();
            var K = Console_.NextInt();


            var xtoy = new Dictionary<long, long>();
            var xary = new long[N];
            for (int i = 0; i < N; ++i)
            {
                var x = Console_.NextLong();
                var y = Console_.NextLong();
                xary[i] = x;
                xtoy[x] = y;
            }
            Array.Sort(xary);

            var ans = 0L;
            for (int i = K - 1; i < N; ++i)
            {
                long maxy = -10000000000;
                long miny = 10000000000;
                for (int j = i - K + 1; j <= i; ++j)
                {
                    var y = xtoy[xary[j]];
                    if (maxy < y) maxy = y;
                    if (miny > y) miny = y;
                }
                var tmpans = (maxy - miny) * (xary[i] - xary[i - K + 1]);
                if (ans == 0 || tmpans < ans) ans = tmpans;
            }

            Console.WriteLine(ans);
        }
    }
}