6731：Angle Beats

Given n points $P_1$, $P_2$, .... , $P_n$ on 2D plane and q queries. In i-th query, a point $A_i$ is given, and you should determine the number of tuples (u, v) that 1 $\leq$ u < v $\leq$ n and $A_i$ , $P_u$, $P_v$ form a non-degenerate right-angled triangle.

The first line contains two positive integers n, q (2 ≤ n ≤ 2 000, 1 ≤ q ≤ 2 000), denoting the numberof given points and the number of queries.
Next n lines each contains two integers xi , yi (|xi|, |yi| ≤ $10^9$), denoting a given point Pi.
Next q lines each contains two integers xi , yi (|xi|, |yi| ≤ $10^9$), denoting a query point Ai.
It is guaranteed that the input n + q points are all pairwise distinct.

Output q lines each contains a non-negative integer, denoting the answer to corresponding query.