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>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define EPS (1e-10)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;
 
int x[50],y[50];
 
signed main(){
	int K,n;cin>>n>>K;
	vector<int>X,Y;
	rep(i,n){
		cin>>x[i]>>y[i];
		X.push_back(x[i]);
		Y.push_back(y[i]);
	}
	ll Min=LLONG_MAX;
	rep(i,X.size())rep(j,X.size()){
		rep(k,Y.size())rep(t,Y.size()){
			int cnt=0;
			rep(l,n){
				if(X[i]<=x[l]&&x[l]<=X[j]&&Y[k]<=y[l]&&y[l]<=Y[t])cnt++;
			}
			if(cnt>=K){
				Min=min(Min,(ll)(X[j]-X[i])*(ll)(Y[t]-Y[k]));
			}
		}
	}
	cout<<Min<<endl;
}