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<cstring>
#include<cstdio>
#include<iostream>
using namespace std;
struct wo{
	long long x;
	long long y;
}a[10001];
long long ans,n,t;
int main(){
    cin>>n>>t;
    for(int i=1;i<=n;i++){
    	cin>>a[i].x>>a[i].y;
	}
	ans=9111111111111111111;
	long long b,c,d,e;
	long long sum=0;
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++){
			for(int k=1;k<=n;k++){
				for(int l=1;l<=n;l++){
					b=a[i].x,c=a[j].x,d=a[k].y,e=a[l].y;
					sum=0;
					if(b>c)swap(b,c);
					if(d>e)swap(d,e);
					for(int m=1;m<=n;m++){
						if(b<=a[m].x&&c>=a[m].x&&d<=a[m].y&&e>=a[m].y){
							sum++;
						}
					}
					if(sum>=t)ans=min(ans,(c-b)*(e-d));
				}
			}
		}
	}
    cout<<ans;
}