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,N) for(int i=n;i<(int)N;i++)
#define RREP(i,n,N) for(int i=N-1;i>=n;i--)
#define p(s) cout<<(s)<<endl
#define ck(n,a,b) ((a)<=(n)&&(n)<=(b))
#define F first
#define S second
typedef long long ll;
using namespace std;
const ll inf=LONG_LONG_MAX;

ll N,K;
ll x[51],y[51];
ll ans;
int main() {
	cin>>N>>K;
	REP(i,0,N){
		cin>>x[i]>>y[i];

	}
	ans=inf;
	REP(i,0,N){
		REP(j,i,N){
			REP(k,j,N){
				REP(l,k,N){
					ll dot=0;
					ll mnx=min(min(x[k],x[l]),min(x[i],x[j]));
					ll mxx=max(max(x[k],x[l]),max(x[i],x[j]));
					ll mny=min(min(y[k],y[l]),min(y[i],y[j]));
					ll mxy=max(max(y[k],y[l]),max(y[i],y[j]));
					REP(n,0,N){
						if(ck(x[n],mnx,mxx)&&ck(y[n],mny,mxy)) dot++;
					}
					if(dot==K){
						ans=min(ans,(mxx-mnx)*(mxy-mny));
					}
				}
			}
		}
	}
	p(ans);
	return 0;
}