Toll Roads
The mayor of a large city has decided to implement a toll on highways that pass through the city to reduce transit traffic. There are n highways in the city's vicinity.
However, the regional administration did not approve the mayor's plan, as truck drivers contribute significantly to the economy of small towns through their patronage of local cafes and hotels.
Consequently, the toll will only apply to highways that actually pass through the city.
The city boasts a well-developed metro system with m metro stations. A highway is considered to pass through the city if at least one metro station is located directly on the highway, or if there is at least one metro station on each side of the highway.
Your task is to help the mayor identify which highways pass through the city.
Input
The first line of the input contains two integers: n and m - the number of highways and the number of metro stations, respectively (1 ≤ n, m ≤ 100000).
The following n lines describe the highways. Each highway is defined by three integers a, b, and c, representing a line on the plane with the equation ax+by+c=0 (|a|, |b|, |c| ≤ 10^6).
The next m lines describe the metro stations. Each station is defined by two integers x and y, representing a point on the plane with coordinates (x, y) (|x|, |y| ≤ 10^6).
Output
The first line of the output should contain a single integer - the number of highways that pass through the city. The second line should list the numbers of these highways in ascending order. Highways are numbered from 1 to n in the order they are provided in the input.