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 (xi, 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.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 x1, x2, ..., xn (1 ≤ xi ≤ 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.Exampleinput
5 5 6 8 3 12
2 6.0 9.87298334621 13.3370849613 12.5187346573 13.3370849613Note
The final positions of the disks will look as follows:
In particular, note the position of the last disk.
var n,r,i,j:longint; x:array[0..1005] of longint; o:array[0..1005] of double;function max(a,b:double):double;begin if a>b then exit(a) else exit(b);end;begin readln(n,r); for i:=1 to n do begin read(x[i]); o[i]:=r; for j:=1 to i-1 do if abs(x[i]-x[j])<=2*r then o[i]:=max(o[i],sqrt(sqr(2*r)-sqr(x[i]-x[j]))+o[j]); end; for i:=1 to n do write(o[i]:0:10,' ');end.