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

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		long min = long.MaxValue;
		for(int i=0;i<N;i++){
			for(int j=i;j<N;j++){
				for(int k=j;k<N;k++){
					for(int l=k;l<N;l++){
					
						long w0 = new long[]{X[i],X[j],X[k],X[l]}.Min();
						long w1 = new long[]{X[i],X[j],X[k],X[l]}.Max();
						long h0 = new long[]{Y[i],Y[j],Y[k],Y[l]}.Min();
						long h1 = new long[]{Y[i],Y[j],Y[k],Y[l]}.Max();
						
						long ar = (w1 - w0) * (h1 - h0);
						if(ar == 0) continue; // 無いはず
						
						int cnt = 0;
						for(int m=0;m<N;m++){
							if(InRange(X[m], w0, w1) && InRange(Y[m], h0, h1)) cnt++;
						}
						if(cnt >= K){
							min = Math.Min(min, ar);
						}
						
					}
				}
			}
		}
			
		Console.WriteLine(min);
		
		
		
		
		
	}
	
	bool InRange(long t, long l, long r){
		return l <= t && t <= r; // inclusive;
	}
	int N,K;
	long[] X,Y;
	public Sol(){
		var d = ria();
		N = d[0]; K = d[1];
		X = new long[N];
		Y = new long[N];
		for(int i=0;i<N;i++){
			d = ria();
			X[i] = d[0];
			Y[i] = d[1];
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}