#include <bits/stdc++.h>
using namespace std;
int a[1500];
double s[1005];
int main() {
  int n, r;
  double c = (double)1.7320508075;
  scanf("%d%d", &n, &r);
  int i, j;
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  for (i = 1; i <= n; i++) {
    s[i] = (double)r;
  }
  s[1] = (double)r;
  for (i = 2; i <= n; i++) {
    for (j = 1; j < i; j++) {
      int x = a[j];
      if (a[i] == a[j]) {
        double d = s[j] + (double)2 * r;
        s[i] = max(s[i], d);
        continue;
      }
      if ((a[i] >= (x - 2 * r)) && (a[i] <= (x + 2 * r))) {
        double k = a[i] - a[j];
        double f = (double)sqrt((double)4 * r * r - (double)(k * k));
        f = f + (double)s[j];
        s[i] = max(s[i], f);
      }
    }
  }
  for (i = 1; i <= n; i++) printf("%.10lf ", s[i]);
}

### 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 a[1500];
double s[1005];
int main() {
  int n, r;
  double c = (double)1.7320508075;
  scanf("%d%d", &n, &r);
  int i, j;
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  for (i = 1; i <= n; i++) {
    s[i] = (double)r;
  }
  s[1] = (double)r;
  for (i = 2; i <= n; i++) {
    for (j = 1; j < i; j++) {
      int x = a[j];
      if (a[i] == a[j]) {
        double d = s[j] + (double)2 * r;
        s[i] = max(s[i], d);
        continue;
      }
      if ((a[i] >= (x - 2 * r)) && (a[i] <= (x + 2 * r))) {
        double k = a[i] - a[j];
        double f = (double)sqrt((double)4 * r * r - (double)(k * k));
        f = f + (double)s[j];
        s[i] = max(s[i], f);
      }
    }
  }
  for (i = 1; i <= n; i++) printf("%.10lf ", s[i]);
}

```