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 pair<int,int> P;
typedef long long ll;
typedef long double ld;
const int inf=1e9+7;
const ll longinf=1LL<<60;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
#define F first
#define S second

const int mx=200010;
const ll mod=1e9+7;

int main() {
  int n,k;
  cin >> n >> k;
  vector<ll> x(n),y(n);
  rep(i,n) cin >> x[i] >> y[i];
  auto a = x, b = y;
  sort(a.begin(),a.end());
  sort(b.begin(),b.end());

  ll ans = longinf*4;
  rep(i,n)REP(j,i+1,n)rep(p,n)REP(q,p+1,n){
    int cnt=0;
    rep(k,n)if(a[i]<=x[k] && x[k]<=a[j] && b[p]<=y[k] && y[k]<= b[q]) cnt++;
    if(cnt >= k){ 
      ll tmp = (a[j]-a[i])*(b[q]-b[p]);
      ans = min(ans, tmp);
    }
  }
  cout << ans << endl;
  return 0;
}