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;

#define reps(i, j, n) for(int i = j; i < (int)n; i++)
#define rep(i, n) reps(i, 0, n)

using int64 = long long;
const int64 INF = 1LL << 62;

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

  cin >> N >> K;
  rep(i, N) {
    cin >> X[i] >> Y[i];
  }

  int64 ret = INF;
  rep(i, N) {
    rep(j, N) {
      rep(k, N) {
        rep(l, N) {
          int inner = 0;
          rep(m, N) inner += X[i] <= X[m] && X[m] <= X[j] && Y[k] <= Y[m] && Y[m] <= Y[l];
          if(inner >= K) ret = min(ret, 1LL * (X[j] - X[i]) * (Y[l] - Y[k]));
        }
      }
    }
  }

  cout << ret << endl;
}