You've got a cookie. This cookie is represented by a convex polygon with n vertices. The vertices of this polygon will be given in counter-clockwise order. Let the area of this polygon be S.

The cookie contains m chocolate chips. Each of them is represented by a point located strictly inside the given polygon.

You are splitting the cookie with a friend. To do that, you can cut along an arbitrary straight line, splitting the cookie into two parts; afterwards, you should give one part to your friend and keep the other for yourself. Chocolate chips that lie exactly on the cut can go to either person.

Let's denote the area of the part of the cookie you get by A and the number of chocolate chips in that part by B.

You really like cookies that are dense with chocolate chips, so you would like to maximize the difference between \(B/m\) and \(A/S\). However, you can't decide how to cut the cookie, so you introduced one more condition: there must be some chocolate chip lying directly on the cut.

For each chocolate chip, compute the maximum value of \(\frac{B}{m} - \frac{A}{S}\) which can be obtained if that chip must lie on the cut.

Constraints

• \(3 \le n \le 400\)

• \(1 \le m \le 400\)

• the coordinates of all points will be at most \(1,000,000\) in absolute value

• all chocolate chips will lie strictly inside the cookie

• the vertices of the cookie will be given in counter-clockwise order

• the cookie will be convex

Input format

The first line of the input contains two space-separated integers n and m.

Each of the following n lines will contain two space-separated integers \(V_{i,x}\) and \(V_{i,y}\) denoting the coordinates of one vertex of the cookie.

Each of the following m lines will contain two space-separated integers \(C_{i,x}\) and \(C_{i,y}\) denoting the coordinates of one chocolate chip. Note that it is possible for the locations of two or more chocolate chips to coincide.

Output format

Print m lines, each containing a single real number. The number on the i-th line should denote the maximum possible value of \(\frac{B}{m}-\frac{A}{S}\) for a cut that goes through the i-th chocolate chip.

Your answer will be accepted if each of these numbers has absolute error at most \(10^{-4}\).