Description

You are given $N$ points in the $xy$-plane. Each point is in a state of linear uniform motion.
Your task is to calculate the distance to the furthest point in Manhattan distance from the origin at time $t$.

Input

The first line of the input file contains the integers $N$ and $M$ ($1 \\leq N, M \\leq 10^5$), separated by a space.
The next $N$ lines describe the points. Each contains four real numbers $x$, $y$, $vx$ and $vy$ ($|x|,|y|,|vx|,|vy| \\leq 10^6$). This shows the initial coordinates $(x, y)$ and velocity $(vx, vy)$.
The next $M$ lines describe the queries. Each line contains one real number $t$ ($0 \\leq t \\leq 10^6$).

Output

For each query, output the maximal Manhattan distance in one line.
The value which is accurate to within a relative or absolute value of 1E-9 will be accepted.

Sample Input

2 2
0 0 1 0
1 0 -1 0
0
1

Sample Output

1.0000000000
1.0000000000

Sample Input

3 3
0 0 1 1
0 1 1 0
3 3 -2 -1
0
1
2

Sample Output

6.0000000000
3.0000000000
4.0000000000

Sample Input

3 3
1 1 0.5 0
0 2 1.5 -1
1.5 0 0 1
0
1
2

Sample Output

2.0000000000
2.5000000000
3.5000000000

Source Name

The First KMCMonthly Contest