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 int long long
#define ll long long
#define rep(i,n) for(int i=0;i<n;i++)
#define INF LLONG_MAX
#define eps LDBL_EPSILON
#define moder 1000000007
#define pie 3.141592653589793238462643383279
#define P std::pair<int,int>
#define prique priority_queue
using namespace std;
int n,k,x[55],y[55];
vector<int> vecx,vecy;
signed main(){
	cin>>n>>k;
	rep(i,n){
		cin>>x[i]>>y[i];
		vecx.push_back(x[i]);
		vecy.push_back(y[i]);
	}
	sort(vecx.begin(),vecx.end());
	sort(vecy.begin(),vecy.end());
	int ans=INF;
	for(int i:vecx){
		for(int j:vecx){
			if(i==j)continue;
			for(int l:vecy){
				for(int m:vecy){
					if(l==m)continue;
					int cnt=0;
					rep(o,n){
						if(i<=x[o]&&x[o]<=j&&l<=y[o]&&y[o]<=m)cnt++;
					}
					if(cnt>=k)ans=min(ans,(j-i)*(m-l));
				}
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}