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;
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007

ll l[52],r[52];
int main() {
	ll n,k,ans=INF;
	cin>>n>>k;
	for(ll i=0;i<n;i++){
		ll x,y;
		cin>>x>>y;
		l[i]=x;r[i]=y;
	}
	for(ll i=0;i<n;i++){
		for(ll j=0;j<n;j++){
			for(ll m=0;m<n;m++){
				for(ll o=0;o<n;o++){
					ll sum=0;
					ll ux=l[i],dx=l[j],uy=r[m],dy=r[o];
					if(ux<dx){
						swap(ux,dx);
					}
					if(uy<dy){
						swap(uy,dy);
					}
					for(ll p=0;p<n;p++){
						ll nowx=l[p],nowy=r[p];
						if(nowx>=dx&&nowx<=ux&&nowy<=uy&&nowy>=dy){
							sum++;
						}
					}
					if(sum>=k){
						ll sq=(ux-dx)*(uy-dy);
						ans=min(ans,sq);
					}
				}
			}
		}
	}
	cout <<ans;
	// your code goes here
	return 0;
}