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 <bits/stdc++.h>
using namespace std;
using ll = long long;

int main()
{
	int N, K;
	cin >> N >> K;
	vector<int> x(N), y(N);
	for (int i = 0; i < N; i++) {
		cin >> x[i] >> y[i];
	}
	ll res = 4000000000000000000ll;
	for (int i = 0; i < N; i++) {
		for (int j = i + 1; j < N; j++) {
			for (int k = 0; k < N; k++) {
				for (int l = k + 1; l < N; l++) {
					ll x0 = min(x[i], x[j]), x1 = max(x[i], x[j]);
					ll y0 = min(y[k], y[l]), y1 = max(y[k], y[l]);
					int cnt = 0;
					for (int m = 0; m < N; m++) {
						if (x0 <= x[m] && x[m] <= x1 && y0 <= y[m] && y[m] <= y1) {
							cnt++;
						}
					}
					if (cnt >= K) {
						res = min(res, (x1 - x0) * (y1 - y0));
					}
				}
			}
		}
	}
	cout << res << endl;
	return 0;
}