#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:99999999")
using namespace std;
long prime[1000001] = {0};
struct dot {
  double x;
  double y;
};
int main() {
  ios_base::sync_with_stdio(0);
  vector<dot> dots;
  dot myD;
  int n;
  cin >> n;
  double x;
  double r;
  cin >> r;
  cin >> x;
  myD.x = x;
  myD.y = r;
  dots.push_back(myD);
  for (int i = 1; i < n; ++i) {
    cin >> x;
    list<dot> variants;
    for (auto a : dots) {
      if (abs(a.x - x) <= 2 * r) variants.push_back(a);
    }
    myD.x = x;
    list<dot> results;
    for (auto a : variants) {
      myD.y = a.y + sqrt(4 * r * r - (a.x - x) * (a.x - x));
      results.push_back(myD);
    }
    double minY = r;
    for (auto a : results)
      if (a.y > minY) minY = a.y;
    myD.y = minY;
    dots.push_back(myD);
  }
  cout << fixed << setprecision(10);
  for (auto a : dots) cout << a.y << " ";
  return 0;
}

### Prompt

Please formulate 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>
#pragma comment(linker, "/STACK:99999999")
using namespace std;
long prime[1000001] = {0};
struct dot {
  double x;
  double y;
};
int main() {
  ios_base::sync_with_stdio(0);
  vector<dot> dots;
  dot myD;
  int n;
  cin >> n;
  double x;
  double r;
  cin >> r;
  cin >> x;
  myD.x = x;
  myD.y = r;
  dots.push_back(myD);
  for (int i = 1; i < n; ++i) {
    cin >> x;
    list<dot> variants;
    for (auto a : dots) {
      if (abs(a.x - x) <= 2 * r) variants.push_back(a);
    }
    myD.x = x;
    list<dot> results;
    for (auto a : variants) {
      myD.y = a.y + sqrt(4 * r * r - (a.x - x) * (a.x - x));
      results.push_back(myD);
    }
    double minY = r;
    for (auto a : results)
      if (a.y > minY) minY = a.y;
    myD.y = minY;
    dots.push_back(myD);
  }
  cout << fixed << setprecision(10);
  for (auto a : dots) cout << a.y << " ";
  return 0;
}

```