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