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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long ull;
typedef long long ll;

struct point {
    ll x,y;
    bool operator < (const point& t) const {
	if( x == t.x )
	    return y < t.y;
	return x < t.y;
    }
};

ull k_in(ll xmin,ll xmax,ll ymin,ll ymax,vector<point> ps, ll K) {
    ll in = 0;
    for(auto& e : ps) {
	if( xmin <= e.x and e.x <= xmax and ymin <= e.y and e.y <= ymax )
	    in++;
    }
    if(K <= in){
	return (ull)(xmax-xmin)*(ull)(ymax-ymin);
    }
    return 18446744073709551610ULL;
}

int main () {
    ll N,K; cin >> N >> K;
    vector<ll> x;
    vector<ll> y;

    vector<point> ps;
    for(ll i=0; i<N; i++) {
	ll a,b; cin >> a >> b;
	x.push_back(a);
	y.push_back(b);
	ps.push_back(point{a,b});
    }
    sort(x.begin(), x.end());
    sort(y.begin(), y.end());
    sort(ps.begin(), ps.end());
	
    ull ans = 18446744073709551610ULL;
    for(int i=0; i<N; i++) {
	for(int j=i+1; j<N; j++) {
	    for(int k=0; k<N; k++) {
		for(int l=k+1; l<N; l++) {
		    ans = min(k_in(x[i],x[j],y[k],y[l],ps,K),ans);
		}
	    }
	}
    }
    cout << ans << endl;
    return 0;
}