#include <bits/stdc++.h>
using namespace std;
map<int, double> use;
inline long double f(int a, int b, int c) {
  long double rez = sqrt((4 * a * a) - ((b - c) * (b - c)));
  return rez;
}
int main() {
  ::ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, r;
  cin >> n >> r;
  const int g = n;
  int x[1005];
  double c;
  int v;
  for (int i = 0; i < n; ++i) cin >> x[i];
  for (int i = 0; i < n; ++i) {
    c = 0;
    v = 0;
    long double curans = 0;
    for (int j = 0; j < i; ++j) {
      if (abs(x[i] - x[j]) <= 2 * r)
        curans = max(f(r, x[i], x[j]) + use[x[j]], curans);
    }
    if (curans == 0) {
      use[x[i]] = r;
      cout << r << " ";
    } else {
      use[x[i]] = curans;
      cout << fixed << setprecision(10) << curans << " ";
    }
  }
}

### Prompt

Create a solution in cpp for 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;
map<int, double> use;
inline long double f(int a, int b, int c) {
  long double rez = sqrt((4 * a * a) - ((b - c) * (b - c)));
  return rez;
}
int main() {
  ::ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, r;
  cin >> n >> r;
  const int g = n;
  int x[1005];
  double c;
  int v;
  for (int i = 0; i < n; ++i) cin >> x[i];
  for (int i = 0; i < n; ++i) {
    c = 0;
    v = 0;
    long double curans = 0;
    for (int j = 0; j < i; ++j) {
      if (abs(x[i] - x[j]) <= 2 * r)
        curans = max(f(r, x[i], x[j]) + use[x[j]], curans);
    }
    if (curans == 0) {
      use[x[i]] = r;
      cout << r << " ";
    } else {
      use[x[i]] = curans;
      cout << fixed << setprecision(10) << curans << " ";
    }
  }
}

```