Sweep line

Marisa wants to run a sweep line algorithm on a set of points. In a sweep line algorithm, the point with the lowest x-value gets processed first, then the 2nd lowest x, then the 3rd, until the point with the highest x gets processed. If 2 points have the same x-value, then they the point with the lower y-value is processed first.

Marisa wonders how the order would change if all the points are rotated. If she rotates all points around the origin by $ang$ degrees counterclockwise, what would be the x-value (after rotation) of the last point processed by a sweep line algorithm?

Since Marisa is studious, she has many values of $ang$ for which she wants the x-value of last point processed.

Input

The first line has 2 integers, $n$, $m$, the number of points, and the number of values of $ang$

The next $n$ lines each have 2 integers, $x_i$ $y_i$, the x and y value of the ith point. All points are distinct.

The next $m$ lines have one value, $ang_i$, a float which gives the amount in degrees the points are rotated by. Each value of $ang_i$ represents an independent case, so do not apply rotations successively.

$1 <= n <= 1e5$

$1 <= m <= 1e4$

$-1e4 <= x_i, y_i <= 1e4$

$0 <= ang_i < 360$

Output:

For every value of $ang_i$, write one line with the answer for that query. The answer being the last x-value processed if the original points were rotated by $ang_i$ degrees counterclockwise.

Sample Input:

3
0 0 
1 1
0 1

Sample Output:

0.2928931713

Sample Input:

4
1 1
3 1
3 4
1 4

Sample Output:

2

Sample Input:

5
0 0
1 0
1 1
0 2
-1 1

Sample Output:

0.1291712523