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:
// ABC075-D
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define rep(i, n, m) for (int (i) = (n); (i) < (m); ++(i))

int main() {
   int N, K;
   ll x[60], y[60];
   cin >> N >> K;
   rep (i, 0, N) cin >> x[i] >> y[i];

   ll area = 1LL << 62;
   rep (xi, 0, N) rep (xj, 0, N) rep (yi, 0, N) rep (yj, 0, N) {
      if (x[xi] <= x[xj] && y[yi] <= y[yj]) {
         int cnt = 0;
         rep (p, 0, N) {
            if (x[p] >= x[xi] && x[p] <= x[xj] && y[p] >= y[yi] && y[p] <= y [yj]) cnt++;
         }

         if (cnt >= K) area = min(area, (x[xj]-x[xi]) * (y[yj]-y[yi]));
      }
   }
   cout << area << endl;

   return 0;
}