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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
  long long N,K,i,j,k,l,m;
  cin >> N >> K;
  long long x[N],y[N];
  for(i=0;i<N;i++) cin >> x[i] >> y[i];
  long long area = -1;
  for(i=0;i<N;i++) {
    for(j=i;j<N;j++) {
      for(k=0;k<N;k++) {
	for(l=k;l<N;l++) {
		int ans = 0;
		for(m=0;m<N;m++) {
			if(x[m]>=min(x[i],x[j])&&x[m]<=max(x[i],x[j])&&y[m]>=min(y[k],y[l])&&y[m]<=max(y[k],y[l])) ans+=1;
		}
		if (ans>=K) {
		  if (area==-1) area = abs((x[i]-x[j])*(y[k]-y[l]));
		  else area = min(area,abs((x[i]-x[j])*(y[k]-y[l])));
		}
	}
      }
    }
  }
  cout << area << endl;
  return 0;
}