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;
int main(){
  long N,K;cin>>N>>K;
  vector<long>X(N),Y(N);for(long i=0;i<N;i++)cin>>X[i]>>Y[i];
  long ans=LONG_MAX;
  for(long a=0;a<N;a++)for(long b=a;b<N;b++)for(long c=b;c<N;c++)for(long d=c;d<N;d++){
    long y1=min(min(Y[a],Y[b]),min(Y[c],Y[d]));
    long y2=max(max(Y[a],Y[b]),max(Y[c],Y[d]));
    long x1=min(min(X[a],X[b]),min(X[c],X[d]));
    long x2=max(max(X[a],X[b]),max(X[c],X[d]));  
    long count=0;
    for(long i=0;i<N;i++)count+=(y1<=Y[i]&&Y[i]<=y2&&x1<=X[i]&&X[i]<=x2);
    if(count>=K)ans=min(ans,(y2-y1)*(x2-x1));
  }
  cout<<ans;
}