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.split.map(&:to_i)
point = []
n.times {point << gets.split.map(&:to_i)}
point.sort!{|a,b| a[0] <=> b[0]}

arr = (0..n-1).to_a
ans = 10 ** 20
arr.combination(2) do |x|
    next if x[1] - x[0] + 1 < k

    arr.combination(2) do |y|
        c = 0
        y.map!{|e| point[e][1]}.sort!

        point[x[0]..x[1]].each do |e|
            c += 1 if y[0] <= e[1] && e[1] <= y[1]
            break if c > k
        end

        next if c != k
        s = (point[x[1]][0] - point[x[0]][0]) * (y[1] - y[0])
        ans = s if ans > s
    end
end

puts ans