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:
/*mohammadreza motabar*/
#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define ll long long
#define pb push_back
typedef pair<int,int> pii;
const ll MAX_N = 1e2,INF = 1e9;
ll x[MAX_N];
ll y[MAX_N];
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int n,k;cin>>n>>k;
	for(int i=1;i<=n;i++)
		cin>>x[i]>>y[i];
	ll ans=1e9;
	ans*=1e9;
	ans*=5;
	for(ll i=1;i<=n;i++)
		for(ll j=1;j<=n;j++)
			for(ll ii=1;ii<=n;ii++)
				for(ll jj=1;jj<=n;jj++){
					ll cnt=0;
					for(ll k=1;k<=n;k++)
						if(x[k]>=x[i]&&x[k]<=x[ii]&&y[k]>=y[j]&&y[k]<=y[jj])
							cnt++;
					if(cnt<k)
						continue;
					ll area=(abs(x[i]-x[ii]))*(abs(y[j]-y[jj]));
					ans=min(area,ans);
				}
	cout<<ans;
}