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;

int n,K;
typedef long long ll;
int px[51];
int py[51];
vector<ll>x;
vector<ll>y;
int main() {
  cin >> n >> K;

  for(int i = 0; i < n; i++) {
    cin >> px[i] >>py[i];
    x.push_back(px[i]);
    y.push_back(py[i]);
  }

  sort(x.begin(),x.end());
  sort(y.begin(),y.end());

  ll ans = (x[n-1] - x[0]) * (y[n-1] - y[0]);
 
  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++) {
	  int tmp = 0;
	  for(int m = 0; m < n; m++) {
	    if(x[i] <= px[m] && px[m] <= x[j] && y[k] <= py[m] && py[m] <= y[l]) tmp++;
	  }
	  
	  if(tmp >= K) ans = min(ans,(x[j] - x[i]) * (y[l] - y[k]));
	  
	  }
	  
      }
    }
  }
  cout << ans << endl;
}