Problem: 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.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#define int long long
using namespace std;

int n, K;
int x[50], y[50];
int xx[50], yy[50];

signed main() {
	int i, j, k, l, m;
	
	cin >> n >> K;
	for (i = 0; i < n; i++) cin >> x[i] >> y[i];
	for (i = 0; i < n; i++) xx[i] = x[i];
	for (i = 0; i < n; i++) yy[i] = y[i];
	sort(xx, xx + n);
	sort(yy, yy + n);
	
	int ans = 5e+18;
	for (i = 0; i < n; i++) {
		for (j = i + 1; j < n; j++) {
			for (k = 0; k < n; k++) {
				for (l = k + 1; l < n; l++) {
					int cnt = 0;
					for (m = 0; m < n; m++) {
						if (xx[i] <= x[m] && x[m] <= xx[j] &&
						    yy[k] <= y[m] && y[m] <= yy[l])
						    	cnt++;
					}
					if (cnt >= K) {
						ans = min(ans, (xx[j] - xx[i]) * (yy[l] - yy[k]));
					}
				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}