Calendar

Handy Smurf created his newest invention: a nanobot calendar. It consists of nanobots showing the current date. Every day, to switch the current date, they have to perform a cyclic rotation by $k$ places, so that a nanobot that was initially at position $i$ is now at position $(i+k) \bmod n$. Nanobots are indexed from $0$. However, nanobots can only understand one command: reverse $l$ $r$, which reverses the positions of all nanobots at positions between $l$ and $r$, so that a nanobot that was initially at position $l$ is now at $r$, the one that was at $l+1$ is now at $r-1$, and so on. Help Handy write an algorithm for updating the date with the minimum number of commands issued.

The first and only line of input contains two integers $n$ and $k$ ($1 \leq n \leq 10^9$, $0 \leq k < n$), specifying the number of nanobots and the number of places to rotate.

The first line of output should contain the integer $m$, the number of reverse commands used. On each of the next $m$ lines, output two integers $a$ and $b$ ($0 \leq a \leq b < n$), which means that the next command is reverse $a$ $b$.