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: Wrong Answer)

N, K = gets.chomp.split(" ").map(&:to_i)

points = []

N.times do
  points << gets.chomp.split(" ").map(&:to_i)
end

dist = []
N.times do |i|
  arr = []
  N.times do |j|
    d = (points[i][0] - points[j][0])**2 + (points[i][1] - points[j][1])**2
    arr << [d, j]
  end
  dist << arr.sort_by{|x| x[0]}
end
ans = []
dist.each do |arr|
  x = []
  y = []
  arr[0..(K-1)].each do |pt|
    x << points[pt[1]][0]
    y << points[pt[1]][1]
  end
  a, b = x.minmax
  c, d = y.minmax
  area = (b - a) * (d - c)
  ans << area.abs
end
puts ans.min