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)

def area(x)
  xx = x.map { |x| x[0] }
  yy = x.map { |x| x[1] }
  return (xx.max-xx.min)*(yy.max-yy.min)
end

n, k = gets.chomp.split.map { |x| x.to_i }
x = []
n.times do |i|
  z = gets.chomp.split(' ').map{ |x| x.to_i }
  x.push(z)
end
a = area(x)
(n-k).times do |i|
  arr = []
  x.length.times do |t|
    new = x[0..t-1] + x[t+1..-1]
    arr.push(area(new))
  end
  a, idx = arr.each_with_index.min
  x = x[0..idx-1] + x[idx+1..-1]
end
puts a