Sherlock is given $2$ square tiles, initially both of whose sides have length $\boldsymbol{l}$ placed in an $x-y$ plane. Initially, the bottom left corners of each square are at the origin and their sides are parallel to the axes.

At $t=0$, both squares start moving along line $y=x$ (along the positive $\boldsymbol{x}$ and $y$) with velocities $\mbox{s1}$ and $\mbox{s2}$.

For each querydetermine the time at which the overlapping area of tiles is equal to the query value, $\textit{queries}[i]$.

Note: Assume all distances are in meters, time in seconds and velocities in meters per second.

Function Description

Complete the movingTiles function in the editor below.

movingTiles has the following parameter(s):

int l: side length for the two squares
int s1: velocity of square 1
int s2: velocity of square 2
int queries[q]: the array of queries

Returns

int[n]: an array of answers to the queries, in order. Each answer will be considered correct if it is at most $\textbf{0.0001}$ away from the true answer.

Input Format

First line contains integers $l,s1,s2$.

The next line contains $\textit{q}$, the number of queries.

Each of the next $\textit{q}$ lines consists of one integer $\textit{queries}[i]$ in one line.

Constraints

$1\leq l,s1,s2\leq10^9$

$1\leq q\leq10^5$

$1\leq\textit{queries}[i]\leq L^2$

$s1\neq s2$

Sample Input

10 1 2
2
50
100

Sample Output

4.1421
0.0000

Explanation

For the first case, note that the answer is around 4.1421356237..., so any of the following will be accepted:

4.1421356237
4.14214
4.14215000
4.1421
4.1422

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