#include <bits/stdc++.h>
using namespace std;
vector<pair<double, double> > a;
pair<double, double> cur;
double r;
void findmax(pair<double, double> p) {
  double y =
      sqrt(2 * r * 2 * r - abs(p.first - cur.first) * abs(p.first - cur.first));
  y += p.second;
  cur.second = max(cur.second, y);
}
void doit(double x) {
  for (double k = 0; k < a.size(); k++) {
    if (abs(x - a[k].first) <= 2 * r) findmax(a[k]);
  }
  a.push_back(cur);
}
int main() {
  double x, n;
  cin >> n >> r;
  for (double k = 0; k < n; k++) {
    cin >> x;
    cur.first = x;
    cur.second = r;
    doit(x);
  }
  for (double k = 0; k < a.size(); k++)
    cout << setprecision(17) << a[k].second << " ";
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
vector<pair<double, double> > a;
pair<double, double> cur;
double r;
void findmax(pair<double, double> p) {
  double y =
      sqrt(2 * r * 2 * r - abs(p.first - cur.first) * abs(p.first - cur.first));
  y += p.second;
  cur.second = max(cur.second, y);
}
void doit(double x) {
  for (double k = 0; k < a.size(); k++) {
    if (abs(x - a[k].first) <= 2 * r) findmax(a[k]);
  }
  a.push_back(cur);
}
int main() {
  double x, n;
  cin >> n >> r;
  for (double k = 0; k < n; k++) {
    cin >> x;
    cur.first = x;
    cur.second = r;
    doit(x);
  }
  for (double k = 0; k < a.size(); k++)
    cout << setprecision(17) << a[k].second << " ";
  return 0;
}

```