Problem D
Asteroid Avoidance

The legendary starship of Flatland, Rectalateral, needs to escape from a star which is about to go supernova by teleporting away. Unfortunately, the possible teleport destinations are in the middle of an asteroid field. Luckily, you have a map of the asteroid field with the exact radius and location of the asteroids (asteroids in Flatland are circles, obviously). As the navigator on board, you must investigate each of the possible teleport destinations and determine if they are safe.

A teleportation destination is safe if and only if no asteroid would touch or overlap Rectalateral immediately after the teleportation completes. Rectalateral will be axis-aligned after the teleportation (the sides of Rectalateral are parallel to the $x$-axis or the $y$-axis).

Input

The first line of input is two integers $ 1\leq w, h \leq 100$, the width and height of the rectangular Rectalateral.

The second line of input is two integers $n, m$, where $1 \leq n \leq 100$ is the number of asteroids in the asteroid field, and $1 \leq m \leq 100$ is the number of potential teleportation destinations.

The next $n$ lines are each three integers $x_ a , y_ a , r_ a$, where $-1000 \leq x_ a , y_ a \leq 1000$ is the location of the center of the circular asteroid and $1 \leq r_ a \leq 100$ is the radius of the asteroid.

The next $m$ lines are each two integers $x_ r,y_ r$, where $-1000 \leq x_ r,y_ r \leq 1000$ is the location of the bottom-left corner of Rectalateral after the teleport. (This means that the top-right corner will be at $(x_ r + w, y_ r + h)$.)

The $x$-axis increases rightwards, and the $y$-axis increases upwards.

Output

For each potential teleportation destination, in the order the teleportation destinations were given, output a single line “DOOMSLUG GO!” if the teleport destination is safe, otherwise output a single line “DOOMSLUG STOP!”.

1 1
2 4
0 0 10
7 9 1
8 6
8 7
8 9
0 0

DOOMSLUG STOP!
DOOMSLUG GO!
DOOMSLUG STOP!
DOOMSLUG STOP!