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 () = Scanf.scanf "%d %d\n" @@ fun n k ->
  let xys = Array.init n @@ fun _ ->
    Scanf.scanf "%d %d\n" @@ fun x y -> x, y in
  Array.sort (fun (v, w) (x, y) -> compare (v, ~- w) (x, ~- y)) xys;
  Printf.printf "%d\n" @@ Array.fold_left (Array.fold_left min) max_int @@
    Array.init (n - k + 1) @@ fun i ->
      Array.init (n - i - k + 1) @@ fun j ->
        let xys' = Array.init (j + k) (fun k -> snd xys.(i + k)) in
        Array.sort compare xys';
        (fst xys.(i + j + k - 1) - fst xys.(i)) * 
        Array.fold_left min max_int (Array.init (j + 1) (fun j -> xys'.(j + k - 1) - xys'.(j)))