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C. New Year and Curling

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputCarol 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.

Input

The first line will contain two integers *n* and *r* (1 ≤ *n*, *r* ≤ 1 000), 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} ≤ 1 000) — the *x*-coordinates of the disks.

Output

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.

Example

Input

6 2

5 5 6 8 3 12

Output

2 6.0 9.87298334621 13.3370849613 12.5187346573 13.3370849613

Note

The final positions of the disks will look as follows:

In particular, note the position of the last disk.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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