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 <image> 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:

<image>

In particular, note the position of the last disk. 
#include <bits/stdc++.h>
using namespace std;
int n, r, x[1005];
double ans[1005];
int main() {
  cin >> n >> r;
  for (int i = 1; i <= n; i++) cin >> x[i];
  for (int i = 1; i <= n; i++) {
    ans[i] = r;
    for (int j = 1; j < i; j++) {
      if (abs(x[i] - x[j]) > 2 * r) continue;
      ans[i] = max(ans[i], ans[j] + sqrt(4.0 * r * r - 1.0 * abs(x[i] - x[j]) *
                                                           abs(x[i] - x[j])));
    }
  }
  for (int i = 1; i <= n; i++)
    cout << fixed << setprecision(9) << ans[i] << ' ';
}
