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;
#define int long long

int x[51],y[51];
vector<int> vx,vy;

signed main(){

  int n,K; cin >> n >> K;
  for(int i = 0; i < n; i++){
    cin >> x[i] >> y[i];
    vx.push_back(x[i]);
    vy.push_back(y[i]);
  }
  sort(vx.begin(),vx.end());
  sort(vy.begin(),vy.end());

  int ans = (1LL << 62);
  for(int i = 0; i < n; i++){
    for(int j = i+1; j < n; j++){
      for(int k = 0; k < n; k++){
        for(int l = k+1; l < n; l++){
          int cnt = 0;
          for(int m = 0; m < n; m++){
            cnt += vx[i] <= x[m] && x[m] <= vx[j] && vy[k] <= y[m] && y[m] <= vy[l];
          }
          if(cnt >= K){
            ans = min(ans,(vx[j]-vx[i])*(vy[l]-vy[k]));
          }
        }
      }
    }
  }
  cout << ans << endl;

  return 0;
}