Angle Beats
Problem Description
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.
Input
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
Output q lines each contains a non-negative integer, denoting the answer to corresponding query.
4 2
0 1
1 0
0 -1
-1 0
0 0
1 1
4
3
Hint
For query (0, 0), the 4 right-angled triangles are
� {(0, 0),(0, 1),(1, 0)}
� {(0, 0),(0, 1),(-1, 0)}
� {(0, 0),(0,-1),(1, 0)}
� {(0, 0),(0,-1),(-1, 0)}
For query (1, 1), the 3 right-angled triangles are
� {(1, 1),(0, 1),(1, 0)}
� {(1, 1),(0, 1),(0,-1)}
� {(1, 1),(1, 0),(-1, 0)}