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>
#include <string>
using namespace std;
#define int long long
int x[100], y[100], ans = -1;
signed main() {
	int n, k; cin >> n >> k;
	for (int i = 0; i < n; i++)cin >> x[i] >> y[i];
	for (int i1 = 0; i1 < n; i1++) {
		for (int i2 = 0; i2 < n; i2++) {
			int xm = min(x[i1], x[i2]), xM = max(x[i1], x[i2]);
			for (int j1 = 0; j1 < n; j1++) {
				for (int j2 = 0; j2 < n; j2++) {
					int ym = min(y[j1], y[j2]), yM = max(y[j1], y[j2]);

					int cnt = 0;
					for (int i = 0; i < n; i++)if (xm <= x[i] && x[i] <= xM && ym <= y[i] && y[i] <= yM)cnt++;
					if (cnt >= k) {
						if (ans < 0)ans = (xM - xm)*(yM - ym);
						else ans = min(ans, (xM - xm)*(yM - ym));
					}
				}
			}
		}
	}
	cout << ans << endl;
}