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.strip.split.map(&:to_i)
xy = readlines.map {|line| line.strip.split.map(&:to_i) }

xy_sorted_x = xy.sort_by {|x,y| x }
xy_sorted_y = xy.sort_by {|x,y| y }

xs = xy.map(&:first).sort
ys = xy.map(&:last).sort

result = (ys.minmax.last-ys.minmax.first) * (xs.minmax.last-xs.minmax.first)

xs.length.times do |lxi|
  (lxi+1...xs.length).each do |rxi|
    lx = xs[lxi]
    rx = xs[rxi]
    next if lx==rx

    diff_x = rx-lx
    ys.length.times do |byi|
      xy_by = xy_sorted_y[byi]
      next if !(lx..rx)===xy_by.first

      by = ys[byi]

      (byi+1...ys.length).each do |tyi|
        ty = ys[tyi]
        diff_y = ty-by
        xy_ty = xy_sorted_y[tyi]
        next if !(lx..rx)===xy_ty.first

        xy_lx = xy_sorted_x[lxi]
        xy_rx = xy_sorted_x[rxi]
        next if !(by..ty)===xy_lx.last || !(by..ty)===xy_rx.last

        if xy.select{|x, y| (by..ty).include?(y) && (lx..rx).include?(x) }.length >= k
          current_result = diff_x * diff_y
          result = current_result if current_result < result
        end
      end
    end
  end
end

p result