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>
#define int long long
using namespace std;

signed main() {
    int N, K;
    cin >> N >> K;

    vector<int> x(N), y(N);
    for (int i = 0; i < N; i++) {
        cin >> x[i] >> y[i];
    }

    int ans = 1LL<<62;
    for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {
        for (int k = 0; k < N; k++) for (int l = 0; l < N; l++) {
            int cnt = 0;
            for (int a = 0; a < N; a++) {
                cnt += !(x[a] < x[i] || x[a] > x[j] || y[a] < y[k] || y[a] > y[l]);
            }
            if (cnt >= K) {
                ans = min(ans, abs(x[i] - x[j]) * abs(y[k] - y[l]));
            }
        }
    }
    cout << ans << endl;

    return 0;
}