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 <iostream>
using namespace std;

using ll = long long;

int main() {
  // 入力
  int N, K;
  cin >> N >> K;
  int x[N], y[N];
  for (int i = 0; i < N; i++) cin >> x[i] >> y[i];

  ll ans = 1LL << 62;
  for (int i = 0; i < N; i++) { // x座標の左端
    for (int j = 0; j < N; j++) { // x座標の右端
      for (int k = 0; k < N; k++) { // y座標の下端
        for (int l = 0; l < N; l++) { // y座標の上端
          if (x[i] > x[j]) continue;
          if (y[k] > y[l]) continue;
          // 4点で作られる長方形に囲まれる点の数を数える
          int cnt = 0;
          for (int m = 0; m < N; m++) {
            if (x[i] <= x[m] && x[m] <= x[j] && y[k] <= y[m] && y[m] <= y[l]) cnt++;
          }

          if (cnt >= K) ans = min(ans, 1LL * (x[j] - x[i]) * (y[l] - y[k]));
        }
      }
    }
  }

  // 解答
  cout << ans << endl;

  return 0;
}