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 rep(i,n) for(int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int MAX_N = 55;
ll X[MAX_N],Y[MAX_N];

int main()
{
	int N,K;
	cin >> N >> K;
	rep(i,N)
	{
		cin >> X[i] >> Y[i];
	}
	ll ans = ll(1e19);
	rep(i,N)
	{
		for(int j = i+1; j < N; ++j)
		{
			rep(k,N)
			{
				for(int l = k+1; l < N; ++l)
				{
					ll x1 = X[i], x2 = X[j], y1 = Y[k], y2 = Y[l];
					if (x1 > x2) swap(x1,x2);
					if (y1 > y2) swap(y1,y2);
					int cnt = 0;
					rep(m,N)
					{
						if (x1 <= X[m] && X[m] <= x2 && y1 <= Y[m] && Y[m] <= y2) cnt++;
					}
					if (cnt >= K)
					{
						ans = min(ans,(x2 - x1) * (y2 - y1));
					}
				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}