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>
#define int long long
using namespace std;

signed main() {
	int N,K;
	cin>>N>>K;
	int c;
	int ans=5000000000000000000;
	std::vector<int> x(N),y(N);
	for(int i=0;i<N;i++)cin>>x[i]>>y[i];
	for(int xi=0;xi<N;xi++){
		for(int xj=xi+1;xj<N;xj++){
			for(int yi=0;yi<N;yi++){
				for(int yj=yi+1;yj<N;yj++){
					c=0;
					for(int i=0;i<N;i++){
						if(min(x[xi],x[xj])<=x[i]&&max(x[xi],x[xj])>=x[i]&&min(y[yi],y[yj])<=y[i]&&max(y[yi],y[yj])>=y[i]){
							c++;
						}
					}
					if(c>=K)ans=min(ans,(max(x[xi],x[xj])-min(x[xi],x[xj]))*(max(y[yi],y[yj])-min(y[yi],y[yj])));
				}
			}
		}
	}
	cout<<ans<<endl;
}