Kill the pig#2504
In a computer game, the goal is to eliminate as many green pigs as possible by launching birds of various colors and flight characteristics from a slingshot.
In this problem, consider a bird with the following flight behavior: immediately after launch, it moves along a parabolic path, as would a projectile thrown at an angle. However, if the player clicks the screen or mouse button, the bird accelerates and continues to fly in a straight line. This straight line is tangent to the parabola at the point where the bird was when the button was pressed.
Treat the screen as a plane with a coordinate grid, and the origin is the bird's starting point. The bird's launch parameters are given: is the angle in degrees between the initial velocity vector and the positive axis, is the bird's speed in meters per second, is the acceleration due to gravity in meters per second squared, and , are the coordinates of the pig in meters. You must determine when the player should accelerate the bird so it will hit the pig. Both the pig and the bird are considered as points. The acceleration due to gravity is directed opposite to the axis. The bird hits the pig if its trajectory intersects the vertical line through the pig's position at a distance no more than 10^{-4} meters from the pig.
The first line contains three integers: , , and — the launch angle, initial speed, and gravitational acceleration respectively (0 < \alpha < 90, 1 \leq V, g \leq 100).
The second line contains two integers and — the pig's coordinates (0 \leq X, Y \leq 100). The pig is not at the origin.
If it is impossible to hit the pig, output Impossible.
If it is possible to hit the pig without acceleration, output Ok.
Otherwise, output a real number — the time in seconds from the bird's start until it must accelerate.
If hitting the pig is possible both with and without acceleration, you may output either option.
A hit is counted when the bird's path intersects the vertical line through the pig's position at a distance no more than 10^{-4} meters from the pig.
Example 1