In return for Petep's present, Reter decides to bake some Christmas cookies for Petep! A cookie can be modelled as a flat Cartesian plane, and Reter has already placed ~N~ chocolate chips at points ~(x_i,y_i)~.

To add the finishing touches to the cookie, Reter wants to add a straight, non-vertical line of icing that passes through at least two of the ~N~ chocolate chips. He would like the chips on the two sides of the line to look as balanced as possible. Thus, he defines the balance value of a non-vertical line ~\ell~ to be the absolute difference between the sum of the vertical distances to ~\ell~ of all points above ~\ell~, and the sum of the vertical distances to ~\ell~ of all points below ~\ell~. The vertical distance of a point ~(x,y)~ to a non-vertical line ~\ell~ is the distance one needs to translate ~(x,y)~ vertically so that it lies on ~\ell~. Reter wonders what the smallest balance value that a non-vertical line passing through at least two of the points is.

However, before adding the line of icing, Reter realizes that Petep might see the cookie from a different direction! Thus, he now has ~Q~ queries. Each query consists of a point ~(a_i,b_i)~, and Reter would like to know: If all the points are rotated about the origin so that ~(a_i,b_i)~ now lies on the positive x-axis, what is the smallest possible balance value?

Constraints

~3 \le N \le 3 \times 10^5~

~1 \le Q \le 3 \times 10^5~

~-10^6 \le x_i, y_i, a_i, b_i \le 10^6~

All ~N~ points ~(x_i,y_i)~ are distinct.

There does not exist a line that contains all ~N~ points ~(x_i,y_i)~.

For all ~1 \le i \le Q~, ~(a_i,b_i) \ne (0,0)~.

Subtask 1 [10%]

~3 \le N \le 2 \times 10^3~

~1 \le Q \le 5~

Subtask 2 [20%]

~3 \le N \le 2 \times 10^3~

~1 \le Q \le 2 \times 10^3~

Subtask 3 [25%]

~3 \le N \le 2 \times 10^3~

Subtask 4 [25%]

~1 \le Q \le 5~

Subtask 5 [20%]

No additional constraints.

Input Specification

The first line contains two space-separated integers: ~N~ and ~Q~.

The next ~N~ lines each contain two space-separated integers: ~x_i~ and ~y_i~.

The next ~Q~ lines each contain two space-separated integers: ~a_i~ and ~b_i~.

Output Specification

Output ~Q~ lines, the answer to each query. Your output will be considered correct if the absolute or relative error of each value does not exceed ~10^{-4}~.

Sample Input 1

4 2
-2 -2
-1 3
2 -1
3 -2
1 0
1 -3

Sample Output 1

3.500000000
3.162277660

Explanation for Sample 1

For the first query, it is optimal to choose the line that passes through the ~1~st and ~3~rd points:

For the second query, it is optimal to choose the line that passes through the ~3~rd and ~4~th points:

Sample Input 2

4 2
-2 2
0 1
1 3
2 0
1 0
2 -1

Sample Output 2

0.000000000
2.236067977

Explanation for Sample 2

For the first query, it is optimal to choose the line that passes through the ~2~nd and ~3~rd points.

For the second query, it is optimal to choose the line that passes through the ~1~st, ~2~nd and ~4~th points.