CF908C.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 = 10100.

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, 10100). 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.

卡罗尔正在玩冰壶游戏。

她在二维平面上有 $ n $ 个半径均为 $ r $ 的圆盘。

初始时，所有这些圆盘均位于直线 $ y = 10^{100} $ 的上方。

接着，她将按编号从 1 到 $ n $ 的顺序，逐个将圆盘向直线 $ y = 0 $ 滑动。

当滑动第 $ i $ 个圆盘时，她先将其圆心置于点 $ (x_i,, 10^{100}) $，然后沿竖直方向向下推动该圆盘（即其 $ x $ 坐标保持恒定，而 $ y $ 坐标持续减小）。该圆盘在碰到直线 $ y = 0 $ 或碰到任意一个先前已停止的圆盘时立即停止。注意：一旦某个圆盘停止运动，它便不再移动，即使之后被其他圆盘碰撞亦然。

请计算所有圆盘全部被推动完毕后，各圆盘圆心的 $ y $ 坐标值。

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.

第一行包含两个整数 $n$ 和 $r$（$1 \leq n, r \leq 1 000$），分别表示圆盘的数量和圆盘的半径。

第二行包含 $n$ 个整数 $x_1, x_2, ..., x_n$（$1 \leq x_i \leq 1 000$）——表示各圆盘的 $x$ 坐标。

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.

输出一行，包含 n 个数字。其中第 i 个数字表示第 i 个圆盘中心的 y 坐标。若输出的绝对误差或相对误差均不超过 10 - 6，则视为正确。

具体而言，假设你对某个坐标值给出的答案为 a，而裁判的标准答案为 b。对于所有坐标，只要满足 ，评测程序即判定你的答案正确。

The final positions of the disks will look as follows:

In particular, note the position of the last disk.

磁盘的最终位置如下所示：

特别注意最后一个磁盘的位置。