Kill the pig
In a computer game, your goal is to launch colorful birds from a slingshot to eliminate as many green pigs as possible. Each bird has unique flight characteristics: initially, it follows a parabolic trajectory like a projectile launched at an angle. However, once the player clicks the screen or mouse button, the bird accelerates and continues in a straight line. This line is tangent to the parabola at the point where the bird was when the button was pressed.
Imagine the screen as a plane with a coordinate grid, where the origin is the bird's starting point. The bird's launch parameters are provided: α — the angle in degrees between the bird's initial velocity vector and the positive OX axis, V — the bird's speed in meters per second, g — the acceleration due to gravity in meters per second squared, and X and Y — the coordinates of the pig in meters. Your task is to determine when the player should accelerate the bird to ensure it hits the pig. Both the pig and the bird are considered as points, and gravity acts in the opposite direction of the OY axis. A hit is achieved when the bird's path intersects the vertical line through the pig's location, within a distance of no more than 10^{-4} meters from the pig.
Input
The first line contains three integers: α, V, and g — the angle of launch, the initial speed, and the gravitational acceleration, respectively (0 < α < 90, 1 ≤ V, g ≤ 100).
The second line contains two integers X and Y — the coordinates of the pig's location (0 ≤ X, Y ≤ 100). The pig is not at the origin.
Output
If hitting the pig is impossible, output Impossible.
If no acceleration is required to hit the pig, output Ok.
Otherwise, output a real number t — the time in seconds from the bird's launch until it should accelerate.
If hitting the pig is possible both with and without acceleration, you may output either option.
A hit is confirmed when the bird's path intersects the vertical line through the pig's location, within a distance of no more than 10^{-4} meters from the pig.