Deleting Numbers

The natural numbers from $1$ to $n$ are written in a row, and a natural number $k$ is given.

One or more steps of deleting numbers in this row are performed. At each step, the remaining numbers are scanned in increasing order, and every $k$-th number is deleted. If fewer than $k$ numbers remain after a step, the deletion process ends.

You must determine at which step the number $n$ is deleted, or find out that it is not deleted before the process ends.

For example, let $n = 13$ and $k = 2$.

• At the first step, the numbers $2, 4, 6, 8, 10, 12$ are deleted, leaving $1, 3, 5, 7, 9, 11, 13$.
• At the second step, the numbers $3, 7, 11$ are deleted, leaving $1, 5, 9, 13$.
• At the third step, the numbers $5, 13$ are deleted, leaving $1, 9$.
• At the fourth step, the number $9$ is deleted, leaving $1$. Since one number remains, the process ends.

Thus the number $13$ is deleted at the third step.

Write a program that, given the numbers $n$ and $k$, determines at which step the number $n$ is deleted.

The first line of the input contains an integer $n$ ($3 \le n \le 10^{18}$).

The second line of the input contains an integer $k$ ($2 \le k \le 100$, $k < n$).

Output a single integer: the number of the step at which the number $n$ is deleted, or $0$ if the number $n$ is not deleted.