#include <bits/stdc++.h>
using namespace std;
const int MAX = 1100;
const int MOD = 1e9 + 7;
class Point {
 public:
  double first, second;
};
Point point[MAX];
double hight[MAX];
int thex[MAX];
bool vis[MAX];
int main() {
  int n, rs;
  scanf("%d %d", &n, &rs);
  int dis;
  for (int i = 0; i < n; i++) {
    scanf("%d", &dis);
    int l = max(1, dis - rs);
    int r = min(dis + rs, 1050);
    double maxs = -1;
    int nowx = 0;
    double nowh = rs;
    bool flag = 0;
    for (int i = l; i <= r; i++) {
      if (vis[i]) flag = 1;
      maxs = hight[i];
      nowx = thex[i];
      nowh = max(nowh, maxs + sqrt(4 * rs * rs - (nowx - dis) * (nowx - dis)));
    }
    if (flag == 0) nowh = rs;
    for (int i = l; i <= r; i++) {
      vis[i] = 1;
      hight[i] = nowh;
      thex[i] = dis;
    }
    printf("%.6lf ", nowh);
  }
}

### 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;
const int MAX = 1100;
const int MOD = 1e9 + 7;
class Point {
 public:
  double first, second;
};
Point point[MAX];
double hight[MAX];
int thex[MAX];
bool vis[MAX];
int main() {
  int n, rs;
  scanf("%d %d", &n, &rs);
  int dis;
  for (int i = 0; i < n; i++) {
    scanf("%d", &dis);
    int l = max(1, dis - rs);
    int r = min(dis + rs, 1050);
    double maxs = -1;
    int nowx = 0;
    double nowh = rs;
    bool flag = 0;
    for (int i = l; i <= r; i++) {
      if (vis[i]) flag = 1;
      maxs = hight[i];
      nowx = thex[i];
      nowh = max(nowh, maxs + sqrt(4 * rs * rs - (nowx - dis) * (nowx - dis)));
    }
    if (flag == 0) nowh = rs;
    for (int i = l; i <= r; i++) {
      vis[i] = 1;
      hight[i] = nowh;
      thex[i] = dis;
    }
    printf("%.6lf ", nowh);
  }
}

```