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)
ps = Array.new
xs = {  }
ys = {  }
N.times do |i|
  x, y = gets.split.map(&:to_i)
  ps[i] = [x,y]
  xs[x] ||= []
  ys[y] ||= []
  xs[x] << i
  ys[y] << i
end

xss = xs.keys.sort
yss = ys.keys.sort
# nx = []
# xss.each_with_index do |x,i|
#   nx[i] = i == 0 ? 0 : nx[i-1]
#   nx[i] += xs[x].size
# end
# ny = []
# yss.each_with_index do |y,i|
#   ny[i] = i == 0 ? 0 : ny[i-1]
#   ny[i] += ys[y].size
# end
result = (xss[-1] - xss[0]) * (yss[-1] - yss[0])
xss.size.times do |right|
  xss.size.times do |left|
    break if right < left
    yss.size.times do |top|
      yss.size.times do |btm|
        break if top < btm
        n = 0
        x = [xss[left], xss[right]]
        y = [yss[btm], yss[top]]
        ps.each do |c|
          n += 1 if c[0] >= x[0] && c[0] <= x[1] && c[1] >= y[0] && c[1] <= y[1]
        end
        # puts [n, x[0], x[1], y[0], y[1]].join(",")
        if n >= K
          result = [result, (x[1] - x[0])*(y[1] - y[0])].min
        end
      end
    end
  end
end
puts result