#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, r;
  cin >> n >> r;
  vector<int> arr(n);
  for (auto &i : arr) cin >> i;
  vector<pair<double, int> > records[1001];
  for (int i = 0; i < n; ++i) {
    double y = r;
    for (int x = max(1, arr[i] - 2 * r); x <= min(1000, arr[i] + 2 * r); ++x)
      if (records[x].size() > 0) {
        y = max(y, records[x].back().first +
                       sqrt((double)(4 * r * r - (arr[i] - x) * (arr[i] - x))));
      }
    records[arr[i]].push_back(make_pair(y, i));
  }
  vector<double> ans(n, 0);
  for (int i = 1; i < 1001; ++i)
    for (auto j : records[i]) ans[j.second] = j.first;
  cout << fixed << setprecision(10);
  for (auto i : ans) cout << i << ' ';
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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() {
  int n, r;
  cin >> n >> r;
  vector<int> arr(n);
  for (auto &i : arr) cin >> i;
  vector<pair<double, int> > records[1001];
  for (int i = 0; i < n; ++i) {
    double y = r;
    for (int x = max(1, arr[i] - 2 * r); x <= min(1000, arr[i] + 2 * r); ++x)
      if (records[x].size() > 0) {
        y = max(y, records[x].back().first +
                       sqrt((double)(4 * r * r - (arr[i] - x) * (arr[i] - x))));
      }
    records[arr[i]].push_back(make_pair(y, i));
  }
  vector<double> ans(n, 0);
  for (int i = 1; i < 1001; ++i)
    for (auto j : records[i]) ans[j.second] = j.first;
  cout << fixed << setprecision(10);
  for (auto i : ans) cout << i << ' ';
  return 0;
}

```