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;
int main(){
  ll n,K;cin>>n>>K;
  ll x[n],y[n];for(ll i=0;i<n;i++)cin>>x[i]>>y[i];
  ll m=5000000000000000000;
  for(ll i=0;i<n-1;i++){
    for(ll j=i+1;j<n;j++){
      for(ll k=0;k<n-1;k++){
        for(ll l=k+1;l<n;l++){
          ll sum=0;
          for(ll a=0;a<n;a++){
            if((x[a]-x[i])*(x[a]-x[j])<=0&&(y[a]-y[k])*(y[a]-y[l])<=0){
              sum++;
            }
          }
          if(sum>=K){
            ll men=abs(x[i]-x[j])*abs(y[k]-y[l]);
            m=min(m,men);
          }
        }
      }
    }
  }
  cout<<m<<endl;
}