P8674 [Lanqiao Cup 2018 National B] Setting the Watch

Xiaoming bought a high-end electronic watch and is getting ready to set the time. In the M78 Nebula, the units of time are different from those on Earth: one hour in the M78 Nebula has $n$ minutes. As everyone knows, the watch has only one button that can increase the current number by $1$. When setting the minutes, if the current displayed number is $0$, pressing the button once changes it to $1$, pressing again changes it to $2$. If the current number is $n-1$, then after pressing once it becomes $0$. Because Xiaoming is very particular, he must set the watch to the exact correct time. If the time on the watch is $1$ minute ahead of the current time, then he needs to press the $+1$ button $n-1$ times to set it back to the correct time. Xiaoming thinks it would be great if the watch could have one more button that adds $k$ to the current number. He wants to know: if there is a $+k$ button, and he presses buttons using the optimal strategy, then from any minute value to any other minute value, what is the maximum number of button presses needed. Note: when pressing the $+k$ button, if the number after adding $k$ exceeds $n-1$, it will be taken modulo $n$. For example, when $n=10,k=6$, if the current time is $0$, then pressing the $+k$ button twice will set it to $2$.

One line with two integers $n,k$, as described above.

One line with one integer, meaning: using the optimal strategy, the maximum number of button presses needed to adjust from one time to another.

**Sample Explanation** If the time is already correct, press $0$ times. Otherwise, the relationship between the number of presses and the sequence of operations is as follows: 1. +1 2. +1, +1 3. +3 4. +3, +1 **Constraints** For $30\%$ of the testdata, $0