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 pair<ll,ll> P;
#define rep(i,m,n) for(int i=m;i<n;i++)
ll mod=1e9+7;

int main(){
  int n,k;
  cin>>n>>k;
  P a[n];
  ll b[n];
  ll c[n];
  rep(i,0,n){
    ll x,y;
    cin>>x>>y;
    a[i]=P(x,y);
    b[i]=x;
    c[i]=y;
  }
  sort(b,b+n);
  sort(c,c+n);
  ll ans=4e19;
  rep(i,0,n-1){
    rep(j,i+1,n){
      rep(h,0,n-1){
        rep(l,h+1,n){
          int cnt=0;
          rep(m,0,n){
            if(b[i]<=a[m].first && a[m].first<=b[j] && c[h]<=a[m].second && a[m].second<=c[l]){
              cnt++;
            }
          }
          if(cnt>=k){
            ans=min(ans,(b[j]-b[i])*(c[l]-c[h]));
          }
        }
      }
    }
  }
  cout<<ans<<endl;
}