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: Accepted)

N,K = $stdin.gets.chomp.split(" ").map{ |a| a.to_i }
pts = (0...N).map{ |i| { i: i, c: $stdin.gets.chomp.split(" ").map{ |a| a.to_i } } }

XS = pts.sort_by{ |pt| pt[:c][0] }

ans = 1000000000*1000000000*4

(0...XS.size-K+1).each { |xs|
  (xs+K-1...XS.size).each{ |xt|
    px = XS[xs..xt].sort_by{ |pt| pt[:c][1] }
    (0...px.size-K+1).each { |ys|
      (ys+K-1...px.size).each{ |yt|
        py = px[ys..yt]
        xx = py.map{ |p| p[:c][0] }
        x = xx.max - xx.min
        y = py[-1][:c][1] - py[0][:c][1]
        ans = [ans, x*y].min
      }
    }
  }
}

puts ans