Aliens

Farmer Ran's cows are grazing happily in their field. Each of the N (1 <= N
<= 100,000) cows has a unique position, represented by an integral coordinate pair.

There are also M (1 <= M <= 1,000,000) one-eyed, cow-loving aliens standing in the field, each with a laser pointer. Each laser pointer emits a ray, and each alien scans the field with his laser, rotating it clockwise until it points to a cow. 

Each laser starts pointing in a direction such that no two cows
are on opposite sides of the laser pointer -- more precisely, at the start, no ray emitted by an alien's laser intersects the line segment between any two cows. Each alien has a favorite cow. Write a program for the aliens to tell them if the first cow seen by each alien will be that alien's favorite cow. No three cows will lie on the same line, and each alien can determine
exactly which cow he is seeing (i.e. there is only one cow lying on his ray
when he stops scanning the field).

PROBLEM NAME: aliens

INPUT FORMAT:

* Line 1: Two integers separated by a space, N and M, representing the
        number of the  cows and the number of the aliens.

* Lines 2..N+1: Two integers X and Y (-1,000,000 <= X,Y <= 1,000,000)
        representing each  cow's position. Cows are numbered with
        integers from 1 to N as they appear  in the input.

* Lines N+2..N+M+1: Three integers separated by spaces that represent
        each alien's position  and the number of his favourite cow.
        The first two integers are smaller  than 10^6 in absolute
        value and the third integer is from 1..N.

SAMPLE INPUT:

3 2
0 0
1 0
0 1
1 1 2
2 2 3

OUTPUT FORMAT:

* Lines 1..M: Line number i contain 1 if the the first cow meet by the
        laser ray of  alien number i is his favourite cow, 0
        otherwise.

SAMPLE OUTPUT:

1
0