시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 256 MB 33 12 12 40.000%

## 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