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)

x = Array.new(N)
y = Array.new(N)
N.times do |i|
  x[i], y[i] = gets.split.map(&:to_i)
end

ans = 4e18

N.times do |i|
  N.times do |j|
    N.times do |k|
      N.times do |l|
        xM = x[i] > x[j]  ? x[i] : x[j]
        xm = x[i] < x[j]  ? x[i] : x[j]
        yM = y[k] > y[l]  ? y[k] : y[l]
        ym = y[k] < y[l]  ? y[k] : y[l]
        cnt = 0
        N.times do |m|
          cnt += 1 if (xm <= x[m] && x[m] <= xM && ym <= y[m] && y[m] <= yM)
        end
        
        s = ( xM - xm ) * ( yM - ym )
        ans = s if ( cnt >= K && s > 0 && ans > s)
      end
    end
  end
end

puts ans