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 rep(i,n) for(int i = 0; i < (int)n; i++)
typedef long long ll;

int main(){
  int n, s;
  cin >> n >> s;
  ll x[n], y[n];
  rep(i, n) cin >> x[i] >> y[i];
  ll ans = 4e18;
  rep(i,n){
    rep(j,n){
      rep(k,n){
        rep(l,n){
          ll xl = min(x[i],x[j]), xr = max(x[i],x[j]);
          ll yl = min(y[k],y[l]), yr = max(y[k],y[l]);
          int c = 0;
          rep(m, n){
            if(x[m] >= xl && x[m] <= xr && y[m] >= yl && y[m] <= yr) c++;
          }
          if(c >= s) ans = min(ans, (xr-xl)*(yr-yl));
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}