시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 256 MB42151539.474%

## 문제

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 ($$v_x + w_x$$, $$v_y + w_y$$) 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.

## 입력

The first line of the input file contains four integers $$S_x$$, $$S_y$$, $$F_x$$, $$F_y$$ — coordinates of start and finish (−10 000 ≤ $$S_x$$, $$S_y$$, $$F_x$$, $$F_y$$ ≤ 10 000).

The second line contains three integers $$n$$, $$k$$ and $$v_{max}$$ — the number of wind condition changes, duration of Jacob’s flight in seconds and maximum aircraft speed (1 ≤ $$n$$, $$k$$, $$v_{max}$$ ≤ 10 000).

The following $$n$$ lines contain the wind conditions description. The $$i$$-th of these lines contains integers $$t_i$$, $$w_{x_i}$$ and $$w_{y_i}$$ — starting at time $$t_i$$ the wind will blow by vector ($$w_{x_i}$$, $$w_{y_i}$$) each second (0 = $$t_1$$ < ··· < $$t_i$$ < $$t_{i+1}$$ < ··· < $$k$$; $$\sqrt{w_{x_i}^2 + w_{y_i}^2}$$ ≤ $$v_{max}$$).

## 출력

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 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.

## 예제 입력 1

1 1 7 4
2 3 10
0 1 2
2 2 0


## 예제 출력 1

Yes
3 2.5
5 2.5
7 4