A11549. New Year and Curling

Carol is currently curling.

She has $n$ disks each with radius $r$ on the 2D plane.

Initially she has all these disks above the line $y=10^{100}$ .

She then will slide the disks towards the line $y=0$ one by one in order from $1$ to $n$ .

When she slides the $i$ -th disk, she will place its center at the point $(x_{i},10^{100})$ . She will then push it so the disk’s $y$ coordinate continuously decreases, and $x$ coordinate stays constant. The disk stops once it touches the line $y=0$ or it touches any previous disk. Note that once a disk stops moving, it will not move again, even if hit by another disk.

Compute the $y$ -coordinates of centers of all the disks after all disks have been pushed.

The first line will contain two integers $n$ and $r$ ( $1<=n,r<=1000$ ), the number of disks, and the radius of the disks, respectively.

The next line will contain $n$ integers $x_{1},x_{2},...,x_{n}$ ( $1<=x_{i}<=1000$ ) — the $x$ -coordinates of the disks.

Print a single line with $n$ numbers. The $i$ -th number denotes the $y$ -coordinate of the center of the $i$ -th disk. The output will be accepted if it has absolute or relative error at most $10^{-6}$ .

Namely, let's assume that your answer for a particular value of a coordinate is $a$ and the answer of the jury is $b$ . The checker program will consider your answer correct if  for all coordinates.

The final positions of the disks will look as follows:

In particular, note the position of the last disk.