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: Accepted)

N, K = gets.split.map(&:to_i)
xs, ys = [], []
N.times do |i|
    xs[i], ys[i] = gets.split.map(&:to_i)
end

xsort = xs.sort
ysort = ys.sort

xmap = {}
ymap = {}
xsort.each_with_index do |x, i|
    xmap[x] = i
end
ysort.each_with_index do |y, i|
    ymap[y] = i
end

imos = Array.new(N){Array.new(N, 0)}
N.times do |i|
    imos[xmap[xs[i]]][ymap[ys[i]]] = 1
end
(1...N).each do |i|
    (0...N).each do |j|
        imos[i][j] += imos[i - 1][j]
    end
end
(1...N).each do |j|
    (0...N).each do |i|
        imos[i][j] += imos[i][j - 1]
    end
end

ans = Float::INFINITY
(0...N).each do |x1|
    ((x1+1)...N).each do |x2|
        (0...N).each do |y1|
            ((y1+1)...N).each do |y2|
                area = (xsort[x2] - xsort[x1]) * (ysort[y2] - ysort[y1])
                next if area >= ans
                points = 0
                points += imos[x1-1][y1-1] if x1 > 0 && y1 > 0
                points += imos[x2][y2]
                points -= imos[x1-1][y2] if x1 > 0
                points -= imos[x2][y1-1] if y1 > 0
                ans = area if points >= K
            end
        end
    end
end

puts ans