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: Time Limit Exceeded)

N,K = gets.split.map(&:to_i)
pts = (0...N).map{ gets.split.map(&:to_i) }
p pts.combination(2).map{ |xx1,xx2|
  x1,_ = *xx1
  x2,_ = *xx2
  x1,x2 = [x1,x2].sort
  pts.combination(2).map{ |yy1,yy2|
    _,y1 = *yy1
    _,y2 = *yy2
    y1,y2 = [y1,y2].sort
    next (1e21).to_i if pts.count{ |x,y| x1 <= x && x <= x2 && y1 <= y && y <= y2 } < K
    (x2-x1)*(y2-y1)
  }.min
}.min