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;

typedef long long ll;
typedef struct {
	ll x,y;
} _pos;
int main () {
	int n,K;cin >> n >> K;
	_pos pos[n];for (int i = 0;i < n;i++) {
		cin >> pos[i].x >> pos[i].y;
	}
	ll ans = 9223372036854775000;
	for (int i = 0;i < n;i++) {
		for (int j = 0;j < n;j++) {
			for (int k = 0;k < n;k++) {
				for (int l = 0;l < n;l++) {
					ll x[]={pos[i].x,pos[j].x,pos[k].x,pos[l].x};
					ll y[]={pos[i].y,pos[j].y,pos[k].y,pos[l].y};
					sort(x,x+4);
					sort(y,y+4);
					int cnt=0;
					for (int m = 0;m < n;m++) {
						if (x[0]<=pos[m].x&&pos[m].x<=x[3]&&y[0]<=pos[m].y&&pos[m].y<=y[3]) {
							cnt++;
						}
					}
					if (cnt>=K) ans = min(ans,(x[3]-x[0])*(y[3]-y[0]));
				}
			}
		}
	}
	cout << ans << endl;
}