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)

def main(argv)
  (n, k) = gets.chomp.split(' ').map(&:to_i)

  p = [nil] * n
  x = [nil] * n
  y = [nil] * n
  n.times do |i|
    (x[i], y[i]) = gets.chomp.split(' ').map(&:to_i)
    p[i] = {:x => x[i], :y => y[i]}
  end
  x.sort!
  y.sort!
  
  s_min = 1e+20.to_i
  n.times do |ix|
    x_min = x[ix]
    
    n.times do |iy|
      y_min = y[iy]
      
      n.times do |jx|
        x_max = x[jx]
        next if x_min >= x_max
        
        n.times do |jy|
          y_max = y[jy]
          next if y_min >= y_max
          
          c = 0
          n.times do |l|
            if x_min <= p[l][:x] && p[l][:x] <= x_max then
              if y_min <= p[l][:y] && p[l][:y] <= y_max then
                c += 1
              end
            end
          end
          
          if c >= k then
            s_min = [s_min, (x_max - x_min) * (y_max - y_min)].min
          end
        end
      end
    end
  end
  
  puts s_min.to_s
end

if self.to_s == 'main' then
  main(ARGV)
end