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 = gets.split.map(&:to_i)
XYs = readlines.map{|l| l.split.map(&:to_i)}

xs, ys = XYs.transpose.map(&:sort)
c = Array.new(N + 1){Array.new(N + 1, 0)}
[*0 ... N].repeated_permutation(2) do |i, j|
  c[i + 1][j + 1] = XYs.count{|x, y| x <= xs[i] && y <= ys[j]}
end
ans = 1e20.to_i
[*[*0 ... N].combination(2)].repeated_permutation(2) do |(i1, i2), (j1, j2)|
  next unless c[i2 + 1][j2 + 1] - c[i2 + 1][j1] - c[i1][j2 + 1] + c[i1][j1] >= K
  s = (xs[i2] - xs[i1]) * (ys[j2] - ys[j1])
  ans = s if s < ans
end
puts ans