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: Wrong Answer)

#if !defined(__clang__) && defined(__GNUC__)
#include <bits/stdc++.h>
#else
#include <cstdlib>
#include <climits>
#include <iostream>
#include <cstdint>
#include <vector>
#include <string>
#include <complex>
#include <bitset>
#include <queue>
#include <deque>
#include <stack>
#include <utility>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <regex>
#endif //  !defined(__clang__) && defined(__GNUG__)
#include <boost/lexical_cast.hpp>
#include <boost/algorithm/string.hpp>
#include <boost/multi_array.hpp>
#include <boost/optional.hpp>
#include <boost/math/common_factor_rt.hpp>

using namespace std;

int main()
{
    int64_t N, K;
    std::cin >> N >> K;

    struct P {
        int64_t x;
        int64_t y;
    };

    std::vector<P> p;
    for (decltype(N) i = 0; i < N; ++i) {
        int64_t x, y;
        std::cin >> x >> y;
        p.push_back({x, y});
    }

    std::sort(std::begin(p), std::end(p),
              [](const auto& a, const auto& b) {
                  return a.x < b.x;
              });

    int64_t S = INT64_MAX;

    for (size_t i = 0; i <= N - K; ++i) {
        // x方向にK個
        auto mm = std::minmax_element(p.begin()+i, p.begin()+i+K,
                                      [](auto a, auto b) {
                                          return a.y < b.y;
                                      });
        auto dd = (p[i+K-1].x - p[i].x) * (mm.second->y - mm.first->y);
        S = std::min(S, dd);
    }

    std::cout << S << std::endl;

    return 0;
}