Joy of Flight
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 airspeed speed 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[w] + w[y]) each second.
Jacob has a fuel for exactly k 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.
Input
The first line contains four integers S[x], S[y], F[x], F[y] (-10000 ≤ S[x], S[y], F[x], F[y] ≤ 10000) - coordinates of start and finish.
The second line contains three integers n, k and v[max] - the number of wind condition changes, durationof Jacob's flight in seconds and maximum aircraft speed (1 ≤ n, k, v[max] ≤ 10000).
The following n lines contain the wind conditions description. The i-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] < ... < k, sqrt(w[xi]^2 + w[yi]^2) ≤ v[max]).
Output
The first line must contain "Yes" if Jacob's plane is able to fly from start to finish in k seconds, and "No" otherwise.
If it can to do that, the following k lines must contain the flight plan. The i-th of these lines must contain two floating point numbers x and y - the coordinates of the position (P[i]) of the plane after i-th second of the flight.
The plan is correct if for every i (1 ≤ i ≤ 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] = S. Moreover the distance between P[k] and F should not exceed 10^(-5) as well.