A university's library has been having electricity issues and students have been struggling to study during nights. They have filed a lot of complaints about it. Finally, after finding a good deal on a lighting option, the university decided to fix the issue.

Each light source can illuminate a circle with a radius of $$r$$, and there are $$n$$ tables in the library and the $$i_{th}$$ table is positioned at point $$(x_{i}, y_{i})$$. Since the university wants to minimize it's expenses, they want to buy the minimum number of light sources. You have to help the university find the minimum number of light sources $$(k)$$, such that each table is illuminated by at least 1 light source.

In other words, your task is to select a minimum number of points $$(k)$$ in the plane, such that for each given point $$(x_{i}, y_{i})$$, there exists a chosen point at a distance of at most $$r$$.

Note: You can place more than one light source at a specific point.

Input format

The first line contains integers $$n$$ and $$r$$ respectively.
In each of the next $$n$$ lines, there are two integers representing $$x_{i}$$ and $$y_{i}$$ respectively that display the position of the \(i_{th}\) table.

Output format

In the first line of output, print an integer $$k$$ that represents the number of light sources.
- Note that the equation $$k \le n$$ must hold.
In each of the next $$k$$ lines, print two decimal numbers representing $$x_{i}, y_{i}$$ respectively that shows the location of the $$i_{th}$$ light source.
- Note that the equation $$|x_i, y_i| \le 10^9$$ must hold.

Constraints
$$1 \le n \le 5 \times 10^3$$
$$1 \le r \le 10^9$$
$$-10^5 \le x_{i}, y_{i} \le 10^5$$

Note: Assume that point $$p$$ is at a distance of at most $$r$$ from point $$q$$, if $$distance(p, q) - r \le 10^{-6}$$ and here, $$distance$$ represents Euclidean distance.