Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define rep(i,x,y) for(int i=x;i<y;i++)
#define range(a) (a).begin(),(a).end()
#define print(A,n) rep(i,0,n){cout<<(i ? " ":"")<<A[i];}cout<<endl;
#define pprint(A,m,n) rep(j,0,m){print(A[j],n);}
const long mod=1e9+7;
const int size=1e5;
const long inf=1e9;
int main(){
	int N,K;cin>>N>>K;
	long X[N+1],Y[N+1]; X[0]=0; Y[0]=0;
	map<long,map<long,int>> cnt;
	rep(i,1,N+1){
		cin>>X[i]>>Y[i]; X[i]+=inf; Y[i]+=inf;
		cnt[X[i]][Y[i]]++;
	}
	sort(X,X+N+1); sort(Y,Y+N+1);
	rep(i,1,N+1)rep(j,1,N+1){
		long x=X[i],y=Y[j];
		cnt[x][y]+=cnt[X[i-1]][y]+cnt[x][Y[j-1]]-cnt[X[i-1]][Y[j-1]];
	}
	long ans=4e18;
	rep(i,1,N+1)rep(j,1,N+1){
		rep(k,i+1,N+1)rep(l,j+1,N+1){
			int temp=cnt[X[k]][Y[l]]-cnt[X[i-1]][Y[l]]-cnt[X[k]][Y[j-1]]+cnt[X[i-1]][Y[j-1]];
			if(temp>=K) ans=min(ans,(X[k]-X[i])*(Y[l]-Y[j]));
		}
	}cout<<ans<<endl;
}