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;
#define rep(i,n) for(int i=0;i<n;i++)
#define rep2(i,a,b) for(int i=(a);i<(b);++i)

template<class T> inline void chmin(T& a, T b) {if (a > b) a = b;}
template<class T> inline void chmax(T& a, T b) {if (a < b) a = b;}

int main() {
  int N,K;
  cin >> N >> K;
  ll x0,x1,y0,y1;
  vector<ll> X(N),Y(N);
  rep(i,N){
    cin >> X[i] >> Y[i];
  }
  ll ans=8*1e18;
  rep(i,N)rep(j,N)rep(k,N)rep(l,N) {
    x0 = min({X[i],X[j],X[k],X[l]});
    x1 = max({X[i],X[j],X[k],X[l]});
    y0 = min({Y[i],Y[j],Y[k],Y[l]});
    y1 = max({Y[i],Y[j],Y[k],Y[l]});
    int cnt=0;
    rep(m,N) {
      if (x0<=X[m]&&X[m]<=x1&&y0<=Y[m]&&Y[m]<=y1) cnt++;
    }
    // cout << cnt << endl;
    if (cnt>=K) chmin(ans,(x1-x0)*(y1-y0));
  }
  cout << ans << endl;
}