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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define REP(i, n) for (int i = 0; (i64)(i) < (i64)(n); ++i)

#ifdef ENABLE_DEBUG
template <typename T>
void debug(T value) {
  cerr << value;
}
template <typename T, typename... Ts>
void debug(T value, Ts... args) {
  cerr << value << ", ";
  debug(args...);
}
#define DEBUG(...)                              \
  do {                                          \
    cerr << " \033[33m (L" << __LINE__ << ") "; \
    cerr << #__VA_ARGS__ << ":\033[0m ";        \
    debug(__VA_ARGS__);                         \
    cerr << endl;                               \
  } while (0)
#else
#define debug(...)
#define DEBUG(...)
#endif

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N, K;
  cin >> N >> K;
  vector<pair<i64, i64>> ps(N);
  vector<i64> xs(N), ys(N);
  REP(i, N) {
    cin >> ps[i].first >> ps[i].second;
    xs[i] = ps[i].first;
    ys[i] = ps[i].second;
  }
  std::sort(ps.begin(), ps.end());
  std::sort(xs.begin(), xs.end());
  std::sort(ys.begin(), ys.end());
  i64 mina = numeric_limits<i64>::max();
  REP(xi, xs.size()) {
    REP(xj, xi) {
      REP(yi, ys.size()) {
        REP(yj, yi) {
          i64 ar =
              (__int128_t)(xs[xi] - xs[xj]) * (__int128_t)(ys[yi] - ys[yj]);
          int cnt = 0;
          REP(k, N) {
            auto [xk, yk] = ps[k];
            if (xk >= xs[xj] && xk <= xs[xi] && yk >= ys[yj] && yk <= ys[yi])
              ++cnt;
          }
          if (cnt >= K) {
            mina = min(mina, ar);
          }
        }
      }
    }
  }
  cout << (i64)(mina) << endl;
}