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;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
const ll inf=5e18;

int main() {
  ll n,K;
  cin >> n >> K;
  vec x(n),y(n);
  for(ll i=0;i<n;i++) {
    cin >> x[i] >> y[i];
  }
  ll ans=inf;
  for(ll i=0;i<n;i++) {
    for(ll j=i+1;j<n;j++) {
      for(ll k=0;k<n;k++) {
        for(ll l=k+1;l<n;l++) {
          ll count=0;
          ll hh=max(y[i],y[j]);
          ll lh=min(y[i],y[j]);
          ll hw=max(x[k],x[l]);
          ll lw=min(x[k],x[l]);
          for(ll m=0;m<n;m++) {
            if(hh>=y[m]&&lh<=y[m]&&hw>=x[m]&&lw<=x[m]) count++;
          }
          if(count>=K) {
            ans=min(ans,(hh-lh)*(hw-lw));
          }
        }
      }
    }
  }
  cout << ans << endl;
}