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)
COORDS= N.times.map { gets.split.map(&:to_i) }

coord_x = []
coord_y = []

COORDS.combination(2).each do |(x1, y1), (x2, y2)|
  coord_x << x1
  coord_x << x2
  coord_y << y1
  coord_y << y2
end

coord_x.sort!
coord_y.sort!

def check(x1, y1, x2, y2)
  cnt = 0

  COORDS.each do |x, y|
    next if x < x1 || x2 < x
    next if y < y1 || y2 < y

    cnt += 1

    if cnt >= K
      return true
    end
  end

  false
end

ans = Float::INFINITY

coord_x.combination(2).each do |x1, x2|
  coord_y.combination(2).each do |y1, y2|
    if check(x1, y1, x2, y2)
      area = (x2 - x1) * (y2 - y1)
      ans = area if ans > area
    end
  end
end

puts ans