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>
typedef long long ll;
using namespace std;

int main() {
  int N,K;
  cin >> N >> K;
  int x[50],y[50];
  int sort_x[50],sort_y[50];
  for (int i=0; i<N; i++) {
    scanf("%d %d",x+i,y+i);
    sort_x[i]=x[i];
    sort_y[i]=y[i];
  }
  sort(sort_x,sort_x+N);
  sort(sort_y,sort_y+N);

  ll ans=4*1e18;
  for (int i=0; i<N-1; i++) {
    for (int j=i+1; j<N; j++) {
      for (int k=0; k<N-1; k++) {
	for (int l=k+1; l<N; l++) {
	  int cnt=0;
	  for (int m=0; m<N; m++) {
	    if (x[m]>=sort_x[i]
		&&x[m]<=sort_x[j]
		&&y[m]>=sort_y[k]
		&&y[m]<=sort_y[l])
	      cnt++;
	  }
	  if (cnt<K) continue;
	  ll s=(ll)(sort_x[j]-sort_x[i])*(sort_y[l]-sort_y[k]);
	  if (s<ans)
	    ans=s;
	}
      }
    }
  }

  cout << ans << endl;
  return 0;
}