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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun solve (n k pos)
  (let ((ret 10000000000000000000000000000000000000000000000000))
    (loop for i below n
          do (let ((vec (make-array 0 :fill-pointer t :adjustable t)))
               (loop for j from i below n
                     for u = 0 for d = (- k 1)
                     do (progn (vector-push-extend (cdr (aref pos j)) vec)
                               (sort vec #'<))
                     do (loop while (< d (length vec))
                              if (>= d (- k 1))
                              do (setf ret (min ret (* (- (aref vec d) (aref vec u)) (- (car (aref pos j)) (car (aref pos i))))))
                              end
                              do (incf u)
                              do (incf d)))))
    ret))

(let* ((n (read))
       (k (read))
       (pos (make-array n :element-type 'cons)))
  (loop for i below n
        do (setf (aref pos i) (cons (read) (read))))
  (princ (solve n k (sort pos #'< :key #'car))))