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: Wrong Answer)

N,K = gets.chomp.split(" ").map(&:to_i)
coord = N.times.map{gets.chomp.split(" ").map(&:to_i)}.sort_by{|i,j|i}
a = Array.new(N+1).map{Array.new(N+1,0)}
ans = 10**20
x,y = 2.times.map{Hash.new}
coord.each_with_index do |b,i|
  x[b[0]] = i+1
end
coord.sort_by{|i,j|j}.each_with_index do |b,i|
  y[b[1]] = i+1
end
coord.each do |i,j|
  a[x[i]][y[j]] = 1
end
x = x.invert
y = y.invert
for i in 1..N
  for j in 1..N
    a[i][j] += a[i][j-1]
  end
end
for i in 1..N
  for j in 1..N
    a[j][i] += a[j-1][i]
  end
end
for i in 1..N-1
  for j in i+1..N
    for k in 1..N-1
      for l in k+1..N
        if a[j][l]+a[i-1][k-1]-a[i-1][l]-a[k-1][j] >= K
          ans = [ans,(x[j]-x[i])*(y[l]-y[k])].min
        end
      end
    end
  end
end
puts ans