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;
long x[50],y[50],N,K,i,j,k,l,m,t,ans=LONG_MAX;
int main(){
  cin>>N>>K;
  for(i=0;i<N;i++)cin>>x[i]>>y[i];
  for(i=0;i<N;i++)for(j=0;j<N;j++)for(k=0;k<N;k++)for(l=0;l<N;l++){
    if(x[i]>=x[j]||y[k]>=y[l])continue;
    t=0;
    for(m=0;m<N;m++)if(x[m]>=x[i] && x[m]<=x[j] && y[m]>=y[k] && y[m]<=y[l])t++;
    if(t>=K)ans=min(ans,(x[j]-x[i])*(y[l]-y[k]));
  }
  cout<<ans<<endl;
}