#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, r;
  cin >> n >> r;
  vector<double> c;
  vector<double> v;
  for (long long i = 0; i < n; i++) {
    double num;
    cin >> num;
    double x, y = 0.0;
    long long f = 0;
    double ans = 0.0;
    for (long long j = 0; j < i; j++) {
      if (v[j] >= num - 2 * r && v[j] <= num + 2 * r) {
        f = 1;
        y = c[j];
        x = v[j];
        double d = (double)(r * r);
        d *= 4;
        d -= (double)((num - x) * (num - x));
        d = (double)(sqrt(d));
        d += y;
        if (d > ans) {
          ans = d;
        }
      }
    }
    if (f == 0) {
      cout << fixed << setprecision(10) << r << " ";
      c.push_back((double)r);
    } else {
      cout << fixed << setprecision(10) << ans << " ";
      c.push_back(ans);
    }
    v.push_back(num);
  }
}

### Prompt

Generate a Cpp solution to the following problem:

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;
int main() {
  long long n, r;
  cin >> n >> r;
  vector<double> c;
  vector<double> v;
  for (long long i = 0; i < n; i++) {
    double num;
    cin >> num;
    double x, y = 0.0;
    long long f = 0;
    double ans = 0.0;
    for (long long j = 0; j < i; j++) {
      if (v[j] >= num - 2 * r && v[j] <= num + 2 * r) {
        f = 1;
        y = c[j];
        x = v[j];
        double d = (double)(r * r);
        d *= 4;
        d -= (double)((num - x) * (num - x));
        d = (double)(sqrt(d));
        d += y;
        if (d > ans) {
          ans = d;
        }
      }
    }
    if (f == 0) {
      cout << fixed << setprecision(10) << r << " ";
      c.push_back((double)r);
    } else {
      cout << fixed << setprecision(10) << ans << " ";
      c.push_back(ans);
    }
    v.push_back(num);
  }
}

```