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 OCaml (4.02.3) (judge verdict: Accepted)

let inf = max_int
let rec for_fold a b f v = if a >= b then v else for_fold (a+1) b f (f v a)
let for_fold_min a b f = for_fold a b (fun x y -> min x (f y)) inf

let () =
  Scanf.scanf "%d %d" @@ fun n k ->
  let c = Array.init n (fun _ -> Scanf.scanf " %d %d" (fun x y -> x, y)) in
  Array.sort compare c;

  let xs = Array.map fst c in Array.sort (-) xs;
  let ys = Array.map snd c in Array.sort (-) ys;

  for_fold_min 0 n (fun i ->
    let ly = ys.(i) in
    for_fold_min i n (fun j ->
      let uy = ys.(j) in
      for_fold_min 0 n (fun h ->
        let lx = xs.(h) in

        let m, ux = Array.fold_left (fun (s, tx) (x, y) ->
          if ly <= y && y <= uy && lx <= x then
            (s+1, if s < k then x else tx)
          else
            (s, tx)) (0, -1) c
        in

        if m >= k then
          ((ux-lx)*(uy-ly))
        else
          inf)))
  |> Printf.printf "%d\n"