Satan Game

A snakes and ladders game is a well-known dice game. At the start, the piece is off the board. At the start of each turn, roll an $M$-sided die. Each natural number from 1 to $M$ comes up with probability $1/M$. Move the piece forward by the number rolled. If the piece is off the board, it moves to the cell matching the rolled number. If the cell has a snake or ladder, the piece moves to the cell it points to. The game ends when the piece reaches cell $N$. Reaching past cell $N$ also counts as finishing.

This problem invites a natural question. "What is the expected number of dice rolls needed to finish?" But we are not solving that problem. We need to build a test case for it.

Create a test case whose answer is 50,000,000,000,000,000,000 or greater.

There is no input.

On the first line, print three natural numbers $N$, $M$, and $S$. $N$ is at most 100, $M$ is at most 20, and $S$ is at most $N/2$.

On each of the next $S$ lines, print the start and end points of one snake or ladder. If the end point is less than the start point, it is a snake. If it is greater, it is a ladder. The start point must be between 1 and $N-1$, and the end point must be between 1 and $N$. No point may repeat among all start and end points.

The game must be finishable no matter which cell the piece is placed on. This includes placing the piece on a cell that cannot be reached at all, or starting on the start of a snake or ladder without taking it. The condition is hard to make sense of, but this is the Gudegi Cup, so go with it.