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 <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <queue>
#include <array>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <cmath>
#include <algorithm>
#include <numeric>
#include <cassert>
#include <utility>
#include <functional>

using namespace std;
using lli = long long int;
template<class T, class U> void init_n(vector<T>& v, size_t n, U x) 
{ v = vector<T>(n, x); }
template<class T> void init_n(vector<T>& v, size_t n) { init_n(v, n, T()); }
template<class T> void read_n(vector<T>& v, size_t n, size_t o = 0) 
{ v = vector<T>(n+o); for (lli i=o; i<n+o; ++i) cin >> v[i]; }
template<class T> void read_n(T a[], size_t n, size_t o = 0)
{ for (lli i=o; i<n+o; ++i) cin >> a[i]; }
template<class T> T gabs(const T& x) { return max(x, -x); }
#define abs gabs

struct Point {
  lli x, y;
};

lli n, k;
vector<Point> p;
vector<lli> xs, ys;
int main() {
  cin >> n >> k;
  init_n(p, n);
  for (lli i=0; i<n; ++i) cin >> p[i].x >> p[i].y;
  for (Point& q : p) {
    xs.push_back(q.x); ys.push_back(q.y);
  }
  sort(begin(xs), end(xs));
  sort(begin(ys), end(ys));

  lli ans = 5e18;
  for (lli xi=0; xi<n; ++xi) {
    for (lli xj=xi+1; xj<n; ++xj) {
      for (lli yi=0; yi<n; ++yi) {
        for (lli yj=yi+1; yj<n; ++yj) {
          lli cnt = 0;
          for (Point& q : p) {
            if (xs[xi]<=q.x && q.x<=xs[xj] 
                && ys[yi]<=q.y && q.y<=ys[yj] && cnt<k) {
              ++cnt;
            }
          }
          if (cnt >= k) ans = min(ans, (xs[xj]-xs[xi])*(ys[yj]-ys[yi]));
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}