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 n, k = Scanf.scanf " %d %d" @@ fun a b -> a, b
let xys = Array.init n @@ fun _ -> Scanf.scanf " %d %d" @@ fun a b -> a, b
let ans, xs, ys = ref max_int, ref [], ref []
let _ = Array.iteri (fun i (xi, yi) -> for j = i + 1 to n - 1 do let xj, yj = xys.(j) in xs := (xi, xj) :: !xs; ys := (yi, yj) :: !ys done) xys; List.(iter (fun (xi, xj) -> iter (fun (yi, yj) -> if Array.fold_left (fun c (x, y) -> if (xi <= x && x <= xj || xj <= x && x <= xi) && (yi <= y && y <= yj || yj <= y && y <= yi) then c + 1 else c) 0 xys >= k then ans := min !ans @@ abs (xi - xj) * abs (yi - yj)) !ys) !xs); Printf.printf "%d\n" !ans