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;
#define INF  (2000000005)
#define BUF (1000)
#define ll long long 

int n,k;
vector<int> x,y;
vector<pair<int,int>> pv;

int main(void){
	cin >> n >> k;

	for(int i=0;i<n;i++){
		int tx,ty;
		cin>>tx>>ty;
		x.push_back(tx);
		y.push_back(ty);
	}	

	ll ans=INF;
	ans*=INF;
	for(auto u1:x) for(auto u2:x){
		for(auto v1:y) for(auto v2:y){
			
			int cnt = 0;
			for(int i=0;i<n;i++){
				if(x[i]>u1&&x[i]>u2) continue;
				if(x[i]<u1&&x[i]<u2) continue;
				if(y[i]<v1&&y[i]<v2) continue;
				if(y[i]>v1&&y[i]>v2) continue;

				cnt++;
			}
			if(cnt>=k){
				ll tmp=(ll)abs(v1-v2)*(ll)abs(u1-u2);
				if(tmp<ans) ans = tmp;
			}				
		}
	}

	cout << ans << endl;
	return 0;
}