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.split.map(&:to_i)
points = []
n.times { points << gets.split.map(&:to_i) }
areas = []
if k < 4
  points.combination(k).each do |combination|
    xs = combination.map { |p| p[0] }.sort
    ys = combination.map { |p| p[1] }.sort
    x_first = xs.first
    x_last = xs.last
    y_first = ys.first
    y_last = ys.last
    inner_points = 0
    points.each_with_index do |(x, y), index|
      inner_points += 1 if x.between?(x_first, x_last) && y.between?(y_first, y_last)
      break if inner_points >= k || inner_points + (n - index - 1) < k
    end
    areas << (x_last - x_first) * (y_last - y_first) if inner_points >= k
  end
  puts areas.min
else
  points.combination(4).each do |a, b, c, d|
    xs = [a[0], b[0], c[0], d[0]].sort
    ys = [a[1], b[1], c[1], d[1]].sort
    x_first = xs.first
    x_last = xs.last
    y_first = ys.first
    y_last = ys.last
    inner_points = 0
    points.each_with_index do |(x, y), index|
      inner_points += 1 if x.between?(x_first, x_last) && y.between?(y_first, y_last)
      break if inner_points >= k || inner_points + (n - index - 1) < k
    end
    areas << (x_last - x_first) * (y_last - y_first) if inner_points >= k
  end
  puts areas.min
end