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>
#include <climits>
#define MAX_N 50
using namespace std;
int n, k;
long long x[MAX_N], y[MAX_N];
long long min(long long a, long long b){
  return a < b ? a : b;
}
int main(void){
  cin >> n >> k;
  for(int i = 0; i < n; i++) cin >> x[i] >> y[i];
  long long ans = LONG_MAX;
  for(int xi = 0; xi < n; xi++){
    for(int xj = 0; xj < n; xj++){
      for(int yi = 0; yi < n; yi++){
        for(int yj = 0; yj < n; yj++){
          long long lx = x[xi];
          long long rx = x[xj];
          long long uy = y[yi];
          long long by = y[yj];
          int cnt = 0;
          for(int i = 0; i < n; i++){
            if(lx <= x[i] && x[i] <= rx && by <= y[i] && y[i] <= uy) cnt++;
          }
          if(cnt >= k) ans = min(ans, (rx-lx)*(uy-by));
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}