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;
using ll=long long;
int main(){
  ll N,K; cin>>N>>K;
  vector<pair<ll,ll>>Z(N);
  vector<ll>X(N),Y(N);
  for(int i=0; i<N; i++){
    ll x,y; cin>>x>>y;
    X[i]=x, Y[i]=y, Z[i]={x,y};
  }
  sort(X.begin(), X.end());
  sort(Y.begin(), Y.end());
  ll ans=4e18+1;
  for(int i=0; i<N-1; i++){
    for(int j=i+1; j<N; j++){
      for(int a=0; a<N-1; a++){
        for(int b=a+1; b<N; b++){
          ll wl=X[i], wh=X[j], hl=Y[a], hh=Y[b], temp=0;
          for(int k=0; k<N; k++){
            if(wl<=Z[k].first && Z[k].first<=wh && hl<=Z[k].second && Z[k].second<=hh) temp++;
          }
          if(temp>=K) ans=min(ans,(wh-wl)*(hh-hl));
        }
      }
    }
  }
  cout<<ans<<endl;
}