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>

#define F first
#define S second

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;

const int N = 55, M = 110;

int n, m;
int x[N], y[N], xx[N], yy[N];

int main()
{
	cin >> n >> m;
	for (int i = 0; i < n; i ++ )
	{
		scanf("%d%d", &x[i], &y[i]);
		xx[i] = x[i], yy[i] = y[i];
	}
	sort(xx, xx + n), sort(yy, yy + n);
	
	LL res = 4e18;
	for (int i = 0; i < n; i ++ )
		for (int j = 0; j <= i; j ++ )
			for (int k = 0; k < n; k ++ )
				for (int l = 0; l <= k; l ++ )
				{
					int cnt = 0;
					for (int u = 0; u < n; u ++ )
						if (x[u] <= xx[i] && x[u] >= xx[j] && y[u] <= yy[k] && y[u] >= yy[l])
							cnt ++ ;
					if (cnt >= m) res = min(res, (LL)(xx[i] - xx[j]) * (yy[k] - yy[l]));
				}
	cout << res << endl;
	return 0;
}