Put a ball in the bottom left corner of a rectangular billiards table, with pockets (holes) in each of the four corners. Then cue the ball in a 45° angle away from the corner pocket. Assume that there is no friction, so the ball never slows down, and also assume that the ball perfectly bounces off at the cushions (in a 90° angle). Where does the ball touch the cushions and in what corner pocket does it disappear?

To describe the positions of the ball, we assume that the billiards table has integer dimensions: the height $$h$$ and the width $$w$$ of the table are natural numbers (the units are not important for this assignment). As indicated in the figure above, we overlay an imaginary coordinate system on top of the billiards table, with the X-axis along the bottom cushion and the Y-axis along the left cushion. This way, we can describe the positions where the ball hits the cushions using $$(x, y)$$-coordinates, where $$x, y \in \mathbb{N}$$ and $$0 \leq x \leq w, 0 \leq y \leq h$$. The origin $$(0, 0)$$ of the coordinate system is in the bottom left pocket of the billiards table.

### Input

Two lines that respectively contain the height $$h \in \mathbb{N}_0$$ and the width $$w \in \mathbb{N}_0$$ of the billiards table.

### Output

Generate a line for each successive cushion hit by the ball, containing the name of the cushion, followed by a space and the $$(x, y)$$ coordinate where the ball hits the cushion. Cushions are named as indicated in the figure above.

Generate a last line containing the name of the pocket where the ball disappears from the table, followed by a space and the $$(x, y)$$ coordinate of that pocket. Pockets are named as indicated in the figure above.

### Example

Input:

6
8

Output:

top cushion (6, 6)
right cushion (8, 4)
bottom cushion (4, 0)
left cushion (0, 4)
top cushion (2, 6)
bottom right pocket (8, 0)

### Epilogue

In 2011 Royal Caribbean1 introduced a self-leveling pool table on its cruise ship Radiance of the Seas2. This video was shot during a storm in the Pacific — gyroscopes inside the table keep the playing surface level so a game can continue even as the ship rolls.