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) }

xs = xy.sort_by {|x,y| x }
ys = xy.sort_by {|x,y| y }

result = (ys[0][-1] - ys[-1][-1]) * (xs[0][0] - xs[-1][0])

n.times do |lxi|
  lx = xs[lxi]
  (lxi+1...n).each do |rxi|
    n.times do |byi|
      by = ys[byi]
      (byi+1...n).each do |tyi|
        rx = xs[rxi]
        ty = ys[tyi]


        next if !(lx[0]..rx[0]).include?(by[0]) || !(lx[0]..rx[0]).include?(ty[0])

        num=0
        xs[lxi..rxi].each do |x, y|
          num+=1 if (by[-1]..ty[-1]).include?(y)
        end
        if num >= k
          current_result = (ty[-1] - by[-1]) * (rx[0] - lx[0])
          result = current_result if current_result < result
        end

      end
    end
  end
end

p result