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)

require 'pp'
require 'set'

n, k = gets.split.map(&:to_i)
points = Array.new(n)
n.times do |i|
    x, y = gets.split.map(&:to_i)
    points[i] = [x, y]
end
points.sort!

# x方向
widths = []
head = 0
tail = k - 1
tail.upto(n-1) do |i|
    widths << points[i][0] - points[head][0]
    head += 1
end

# y方向
heights = []
head = 0
tail = k - 1
memo = SortedSet.new((head..tail).map{|x| points[x][1] })
heights << memo.max - memo.min
tail += 1
tail.upto(n-1) do |i|
    memo.delete(points[head][1])
    memo << points[i][1]
    heights << memo.max - memo.min
    head += 1
end

min = widths[0] * heights[0]
widths.each_with_index do |w, i|
    s = w * heights[i]
    if s < min
        min ||= s
    end
end

puts min