# Japan Alumni Group Summer Camp 2013 Warming Up

## G - Moving Points

Time limit時間制限 : 1.5sec / Memory limitメモリ制限 : 96MB

### 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