Safe Area

The screen is the rectangle whose lower left corner is $(0, 0)$ and whose upper right corner is $(W, H)$. The player moves a machine shaped as a circle of radius $R$, and the machine has to stay completely inside the screen.

Enemies fire laser beams from outside the screen. A warning line is drawn a few seconds before a beam is fired along it, so the path of every beam is known in advance. The $i$-th warning line is the infinite straight line through the two distinct points $(x_{i,1}, y_{i,1})$ and $(x_{i,2}, y_{i,2})$, and the beam fired along that line covers every point whose distance to the line is at most $t_i$.

The machine is destroyed once it overlaps a beam. A machine centred at $(x, y)$ therefore survives exactly when both of the following hold.

• $R \le x \le W - R$ and $R \le y \le H - R$.
• For every $i$, the distance from $(x, y)$ to the $i$-th line is at least $t_i + R$.

If at least one such position exists, the screen has a safe area. Given the warning lines and the radius of the machine, decide whether a safe area exists.

The input is a sequence of datasets. Each dataset has the following format.

W H N R
x1,1 y1,1 x1,2 y1,2 t1
x2,1 y2,1 x2,2 y2,2 t2
...
xN,1 yN,1 xN,2 yN,2 tN

The first line contains four integers $W$, $H$, $N$ and $R$ ($2 < W \le 640$, $2 < H \le 480$, $0 \le N \le 100$, $0 < R < \min(W, H) / 2$). $W$ and $H$ are the width and the height of the screen, $N$ is the number of laser beams, and $R$ is the radius of the machine.

The $i$-th of the next $N$ lines contains the integer coordinates of two distinct points on the $i$-th warning line, followed by the thickness $t_i$ of that beam ($0 \le t_i \le 1000$). Every coordinate is an integer point on the screen ($0 \le x \le W$, $0 \le y \le H$). The centre of the machine may sit at non-integer coordinates.

There are at most 50 datasets, and the last line of the input is 0 0 0 0. Do not process that line.

In every dataset the answer stays the same if the radius of the machine grows by $10^{-5}$.

For each dataset, print Yes on one line if a safe area exists, and No otherwise.