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>
#include <assert.h>

using namespace std;

int main()
{
	int n, k;
	cin >> n >> k;
	vector<long long> x(n), y(n);
	for (int i = 0; i < n; i++)
		cin >> x[i] >> y[i];
	long long ans = LLONG_MAX;
	for (int xt = 0; xt < n; xt++)
		for (int xu = 0; xu < n; xu++)
			for (int yl = 0; yl < n; yl++)
				for (int yr = 0; yr < n; yr++)
				{
					int cnt = 0;
					for (int i = 0; i < n; i++)
						if (x[xu] <= x[i] && x[i] <= x[xt] && y[yl] <= y[i] && y[i] <= y[yr])
							cnt++;
					if (k <= cnt)
						ans = min(ans, abs(x[xt] - x[xu]) * abs(y[yr] - y[yl]));
				}
	cout << ans << endl;

	return 0;
}