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()
{
  int64_t N, K, ans = (1LL << 62);
  cin >> N >> K;
  vector<int64_t> X(N), Y(N);
  for (int i = 0; i < N; i++)
  {
    cin >> X[i] >> Y[i];
  }
  for (int i = 0; i < N; i++) // left
  {
    for (int j = 0; j < N; j++) // right
    {
      if (X[i] >= X[j])
        continue;
      for (int k = 0; k < N; k++) // top
      {
        for (int l = 0; l < N; l++) // bottom
        {
          if (Y[k] <= Y[l])
            continue;
          int64_t cnt = 0;
          for (int m = 0; m < N; m++)
          {
            if (X[i] <= X[m] && X[m] <= X[j] && Y[l] <= Y[m] && Y[m] <= Y[k])
              cnt++;
          }
          if (cnt >= K)
            ans = min(ans, (X[j] - X[i]) * (Y[k] - Y[l]));
        }
      }
    }
  }
  cout << ans << endl;
}