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)

N, K = gets.chomp.split.map(&:to_i)
XYS = readlines.map { |l| l.chomp.split.map(&:to_i) }

sorted_x = XYS.sort_by { |xy| xy[0] }
sorted_y = XYS.sort_by { |xy| xy[1] }

ans = (sorted_x[-1][0] - sorted_x[0][0]) * (sorted_y[-1][1] - sorted_y[0][1])

N.times do |xi|
  (xi+1...N).each do |xj|
    N.times do |yi|
      (yi+1...N).each do |yj|
        num = 0

        lx = sorted_x[xi][0]
        rx = sorted_x[xj][0]

        by = sorted_y[yi][1]
        uy = sorted_y[yj][1]

        sorted_x[xi..xj].each do |x, y|
          num += 1 if by <= y && y <= uy
        end
        ans = [ans, (rx - lx) * (uy - by)].min if num >= K
      end
    end
  end
end

p ans