Joy of Flight#7501
Jacob likes to play with his radio-controlled aircraft. The weather today is pretty windy and Jacob has to plan flight carefully. He has a weather forecast - the speed and direction of the wind for every second of the planned flight.
The plane may have airspeed up to v_{max} units per second in any direction. The wind blows away plane in the following way: if the airspeed of the plane is (v_x, v_y) and the wind speed is (w_x, w_y), the plane moves by (v_x + w_x, v_y + w_y) each second.
Jacob has a fuel for exactly seconds, and he wants to learn, whether the plane is able to fly from start to finish in this time. If it is possible he needs to know the flight plan: the position of the plane after every second of flight.
The first line contains four integers S_x, S_y, F_x, F_y (-10000 \le S_x, S_y, F_x, F_y \le 10000) - coordinates of start and finish.
The second line contains three integers , and v_{max} - the number of wind condition changes, durationof Jacob's flight in seconds and maximum aircraft speed (1 \le n, k, v_{max} \le 10000).
The following lines contain the wind conditions description. The -th of these lines contains integers t_i, w_{xi} and w_{yi} - starting at time t_i the wind will blow by vector (w_{xi}, w_{yi}) each second(0 = t_1 < ... < t_i < t_{i+1} < ... , \sqrt{w_{xi}^2 + w_{yi}^2} \le v_{max}).
The first line must contain "Yes" if Jacob's plane is able to fly from start to finish in seconds, and "No" otherwise.
If it can do that, the following lines must contain the flight plan. The -th of these lines must contain two floating point numbers and - the coordinates of the position (P_i) of the plane after -th second of the flight.
The plan is correct if for every (1 \le i \le k) it is possible to fly in one second from P_{i-1} to some point Q_i, such that distance between Q_i and P_i doesn't exceed 10^{-5}, where P_0 = . Moreover the distance between P_k and should not exceed 10^{-5} as well.
Example 1