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 int long long
#define rep(i,n) for(int i=0;i<n;i++)
const long long mod = 1000000007;
const double eps = 1e-11;
const int inf = 1ll << 62;

int x[55],y[55];

signed main(){
	int n,K;cin>>n>>K;
	rep(i,n)cin>>x[i]>>y[i];
	vector<int>xa,ya;
	rep(i,n){
		xa.push_back(x[i]);
		ya.push_back(y[i]);
		}
	sort(xa.begin(),xa.end());
	sort(ya.begin(),ya.end());
	int res=inf;
	rep(i,n){
		for(int j=i+1;j<n;j++){
			rep(k,n){
				for(int l=k+1;l<n;l++){
					int cnt=0;
					rep(m,n){
						if(xa[i]<=x[m]&&x[m]<=xa[j]&&ya[k]<=y[m]&&y[m]<=ya[l]){
							cnt++;
							}
						}
					if(cnt>=K){
						res=min(res,(ya[l]-ya[k])*(xa[j]-xa[i]));
						}	
					}
				}
			}
		}
		cout<<res<<endl;
	}