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.map(&:first).uniq.sort
ys = xy.map(&:last).uniq.sort

result = (ys.minmax.last-ys.minmax.first) * (xs.minmax.last-xs.minmax.first)

selected_xs = []
xs.combination(2).select do |x1, x2|
  x1 , x2 = [x1, x2].minmax
  selected_xs.push([x1 , x2]) if xy.select {|x, y| (x1..x2)===x }.length >= k
end

selected_ys = []
ys.combination(2).select do |y1, y2|
  y1 , y2 = [y1, y2].minmax
  selected_ys.push([y1, y2]) if xy.select {|x, y| (y1..y2)===y }.length >= k
end

selected_xs.each do |x1, x2|
  diff_x = x2-x1
  selected_ys.each do |y1, y2|
    diff_y = y2-y1

    if xy.select {|x, y| (x1..x2)===x && (y1..y2)===y }.length >= k
      current_result = diff_x*diff_y
      result = current_result if current_result < result
    end
  end
end

p result