Tennis
ping?
pong
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ICMP Protocol
Alina isn't fond of watching TV, but she turns it on to play the built-in "tennis" game with her younger brother, Boris.
Here's how the game works: a ball, represented as a point, moves across a rectangular playing field with dimensions 2w×2h. At the start of the game, the ball is positioned at the center of the field (coordinates (0, 0)) and moves with a velocity of (x_v, y_v). The players control "rackets," which are vertical segments of lengths a and b. Initially, Alina's racket is positioned at (-w, a/2) to (-w, -a/2), and Boris's racket is at (w, b/2) to (w, -b/2). These rackets can move along the y axis at a speed of v_r.
When the ball hits a horizontal boundary of the field, it bounces off at the same angle, maintaining its speed. If it hits a racket (including its edge), it also bounces off at the same angle, but its speed increases by 10% of its current speed. If the ball hits a vertical boundary without hitting a racket, the player on that side loses: Alina loses if the ball hits the left boundary, and Boris loses if it hits the right boundary. The game is considered a draw if each player has hit the ball with their racket n times.
Given the dimensions of the field, the parameters of the rackets, the initial speed of the ball, and the number n, determine the winner with optimal play.
Input
The first line of input provides the integers w and h (1 ≤ w, h ≤ 10^4). The second line provides x_v and y_v (1 ≤ |x_v| ≤ 10^4, 1 ≤ |y_v| ≤ 10^4). The third line provides a and b (1 ≤ a, b ≤ 2h). The fourth line provides v_r (1 ≤ v_r ≤ 10^4) and n (1 ≤ w, h ≤ 100).
Output
Print "First" if Alina wins, "Second" if Boris wins, or "Draw" if the game ends in a draw.