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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

$stdin.read.split(?\n).map { |line| line.split(?\s).map(&:to_i) }.tap do |(_, k), *ls|
  ps = []
  ls.each do |x, y|
    ps << [x, y]
  end

  min_size = 1.0/0
  ps.each do |a|
    ps.each do |b|
      ps.each do |c|
        ps.each do |d|
          xs = [a[0], b[0], c[0], d[0]]
          ys = [a[1], b[1], c[1], d[1]]
          max_x = xs.max
          min_x = xs.min
          max_y = ys.max
          min_y = ys.min
          if ps.select { |x, y| min_x <= x && x <= max_x && min_y <= y && y <= max_y }.length >= k
            size = (max_x - min_x) * (max_y - min_y)
            min_size = min_size < size ? min_size : size
          end
        end
      end
    end
  end
  puts min_size
end