A. Attacking Bees
time limit per test
4 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

The city of Rio de Janeiro is under attack! By a swarm of bees? That act in a very specific manner? That's correct, and unfortunately, MatheusAB has been caught in the middle of this mess. Luckily for him though, he was able to find a bunker in time to hide in and for some reason he has a special device that is able to track the location and direction of the bees. As previously mentioned, they behave in a very specific way: there are $$$n$$$ queen bees that command a swarm of millions of bees and they will attack anything that is present in the smallest convex polygon that contains all the queen bees.

With MatheusAB's special device, he's able to track the location of the queen bees, and he realizes that each of them has a specific constant velocity and direction. Since he's exhausted from this situation, given the initial positions of the queen bees, he asks you to help him find out what's the minimum amount of time he'll have to wait in order for the city to be safe to roam in again. Initially, all queen bees are within city limits. Rio de Janeiro is considered safe once there aren't any areas within it that are susceptible to a bee attack. The city is conveniently a convex polygon defined by $$$m$$$ vertices.

Input

The first line contains two integers, $$$n$$$, $$$m$$$, $$$(1 \leq n \leq 10^5)$$$, $$$(3 \leq m \leq 10^5)$$$ — the number of queen bees and the number of vertices that define the city.

Each of the next $$$n$$$ lines will contain the description of the queen bee. Each line contains four integers, $$$x_i$$$, $$$y_i$$$, $$$vx_i$$$, $$$vy_i$$$, $$$(-10^9 \leq x_i, y_i \leq 10^9)$$$, $$$(-10^7 \leq vx_i, vy_i \leq 10^7)$$$ — the position in the x and y coordinates and their respective velocities. The velocity is given in units per second. It is guaranteed that each queen bee starts within city limits.

Each of the next $$$m$$$ lines will contain two integers, $$$x_j$$$, $$$y_j$$$, $$$(-10^9 \leq x_j, y_j \leq 10^9)$$$ — the coordinates of the $$$j^{th}$$$ vertex that describes the city.

Output

If the city is forever under attack, print the word rip in a single line.

Otherwise, output a real number — the minimum amount of time (in seconds) MatheusAB will have to wait. Your answer will be considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$, that being if your answer is $$$a$$$ and the jury's is $$$b$$$, then the judge will check if $$$\frac{|a - b|}{max(1, b)} \leq 10^{-6}$$$.

Examples
Input
3 3
-3 0 -1 0
0 -3 1 1
0 3 1 1
-5 0
0 5
0 -5
Output
12
Input
3 3
-3 0 -1 0
0 -3 -1 -1
0 3 1 1
-5 0
0 5
0 -5
Output
rip
Note
The following image describes the first test case. The polygon in red is the city, the polygon in blue describes the initial position of the queen bees and the green polygon represents their area at time $$$\approx 12$$$.

For the second test case, it is easy to see that the bees will always be attacking the city.