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;

using int64 = long long;

int main()
{
  int N, K, X[50], Y[50];

  cin >> N >> K;
  vector< int > aa, bb;
  for(int i = 0; i < N; i++) {
    cin >> X[i] >> Y[i];
    aa.push_back(X[i]);
    bb.push_back(Y[i]);
  }

  int64 ret = numeric_limits< int64 >::max();
  for(int i : aa) {
    for(int j : aa) {
      for(int k : bb) {
        for(int l : bb) {

          int beet = 0;
          for(int m = 0; m < N; m++) {
            beet += i <= X[m] && X[m] <= j && k <= Y[m] && Y[m] <= l;
          }
          if(beet >= K) {
            ret = min(ret, 1LL * (j - i) * (l - k));
          }
        }
      }
    }
  }

  cout << ret << endl;

}