Aliens! aliens.X Farmer John's cows are grazing happily in the field. Each of the N (1 <= N <= 100,000) cows has a unique position, represented by a coordinate pair. There are also M (1 <= M <= 1,000,000) 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. That is, 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