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 main(){
  int i, j, k, m, l;
  int N, K;
  long long x[50], y[50];
  long long x1, x2, y1, y2, cnt;
  long long area = LLONG_MAX;

  cin >> N >> K;

  for(i = 0; i < N; i++)
    cin >> x[i] >> y[i];

  for(i = 0; i < N; i++){
    for(j = 0; j < N; j++){
      for(k = i+1; k < N; k++){
        for(l = j+1; l < N; l++){
          x1 = max(x[i], x[k]);
          x2 = min(x[i], x[k]);
          y1 = max(y[j], y[l]);
          y2 = min(y[j], y[l]);

          cnt = 0;
          for(m = 0; m < N; m++){
            if(x[m] <= x1 && x[m] >= x2 && y[m] <= y1 && y[m] >= y2){
              cnt++;
            }
          } 
          if(cnt >= K && (x1-x2)*(y1-y2) < area)
            area = (x1-x2)*(y1-y2);
        }
      }
    }
  }

  cout << area << endl;

  return 0;
}