Coin Game

Now it's time to play a real game! But, I don't have anything but just one little coin. So, let's do something fun with it!

This isn't just any ordinary coin; it bears a unique image allowing me to interpret its rotational angle with remarkable ease. By selecting a specific point on this coin's face, I can draw an arrow from the center to that point. Intrigued? I thought you would be! Let's set the stage for our game.

Imagine this: I place the coin right at the origin on a two-dimensional coordinate plane, poised to face along the positive $Oy$ axis. The game is turn-based. On each turn, the active player will rotate the coin by one of the four predetermined angles, then advance it by 1 unit in the direction defined by the arrow.

The game lasts for $500$ full moves ($500$ turns for one player and $500$ for the other). After all moves, you win if the $x$ coordinate of the coin is negative, and I win otherwise.

The rotation options available depend on the current coordinates of the coin $(x, y)$ and are computed with the following formulas:

1. $\alpha\_1 = \sqrt{x^2 + y^2} + x^2 + A \cdot |x|$
2. $\alpha\_2 = \sqrt{x^2 + y^2} - x^2 - B \cdot |x|$
3. $\alpha\_3 = \sqrt{x^2 + y^2} + y^2 + C \cdot |y|$
4. $\alpha\_4 = \sqrt{x^2 + y^2} - y^2 - D \cdot |y|$

Here, $A$, $B$, $C$, and $D$ are some constants established before the game begins.

Excited yet? What's that? You're unsure about how to conquer this challenge? You think just because I conceived this game, I have all the strategies figured out? Fear not! I'll grant you a small advantage: I'll make my moves in the blink of an eye.

The example is provided to demonstrate the format of input and output. In the actual validation of the solution, players will make $500$ moves and the jury's program will output all numbers with a precision of $18$ decimal places.

To avoid precision issues, you may use the coin-moving function from the jury's program:

double pi = acos(-1.);

void rotate_and_move(double &x, double &y, double &a, int type) {
    double diff = 0;
    double s = sqrt(x * x + y * y);
    if (type == 1) diff = s + x * x + A * fabs(x);
    if (type == 2) diff = s - x * x - B * fabs(x);
    if (type == 3) diff = s + y * y + C * fabs(y);
    if (type == 4) diff = s - y * y - D * fabs(y);
    a += diff;
    a = fmod(a, 2 * pi);
    x += cos(a);
    y += sin(a);
}