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)

// ABC 075 D Axis-Parallel Rectangle

using System;
using System.Linq;

class Program
{
    static int N;
    static int K;
    static int[] x;
    static int[] y;

    static void Main()
    {
        /* 入力の受け取り */
        int[] input = Console.ReadLine().Split().Select(int.Parse).ToArray();
        N = input[0];
        K = input[1];
        x = new int[N];
        y = new int[N];
        for (int i = 0; i < N; i++)
        {
            input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            x[i] = input[0];
            y[i] = input[1];
        }

        /* a,c in xかつb,d in y の場合を全探索 */
        long ans = long.MaxValue;
        foreach (var a in x)
        {
            foreach (var c in x)
            {
                foreach (var b in y)
                {
                    foreach (var d in y)
                    {
                        if (Judge(a, b, c, d))
                            ans = Math.Min(ans, (long)(c - a) * (b - d));
                    }
                }
            }
        }
        Console.WriteLine(ans);
    }

    /* 左上の座標が(a,b), 右下の座標が(c,d)の長方形が、K個以上の点を含むか */
    static bool Judge(int a, int b, int c, int d)
    {
        if (a >= c || d >= b) return false;
        int count = 0;
        for (int i = 0; i < N; i++)
        {
            int xi = x[i];
            int yi = y[i];
            if (a <= xi && xi <= c && d <= yi && yi <= b)
                count++;
        }
        if (count >= K) return true;
        return false;
    }
}