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, *rest = $stdin.read.split.map(&:to_i)
POINTS = rest.each_slice(2).map.with_index(0){|(x, y), i| [i, x, y]}

XPOINTS = POINTS.sort_by{|i, x, y| x}
YPOINTS = POINTS.sort_by{|i, x, y| y}

ans = Float::INFINITY
n_cases = 0
for _l in 0...N
  l = XPOINTS[_l]
  for _r in (_l+1)...N
    r = XPOINTS[_r]
    next if l[1] == r[1]  # 横幅が0でないこと
    for _b in 0...N
      b = YPOINTS[_b]
      next if b[1] < l[1] || b[1] > r[1]   # bがl-r間にあること
      for _t in (_b+1)...N
        t = YPOINTS[_t]
        next if b[2] == t[2]  # 縦幅が0でないこと
        next if t[1] < l[1] || t[1] > r[1]  # tがl-r間にあること
        next if l[2] < b[2] || l[2] > t[2] # lがb-t間にあること
        next if r[2] < b[2] || r[2] > t[2] # rがb-t間にあること

        n_points = 0
        max_x = r[1]
        _l.upto(_r) do |i|
          y = XPOINTS[i][2]
          n_points += 1 if y >= b[2] && y <= t[2]
          break if n_points >= K
        end
        next if n_points < K

        area = (r[1] - l[1]) * (t[2] - b[2])
        #p l: l, r: r, t: t, b: b, n_points: n_points, area: area
        ans = area if area < ans

        n_cases += 1
      end
    end
  end
end
#p n_cases: n_cases
p ans