Map

The hooligan Vasya got an F in geography and, out of anger, started tearing up a map. He did this for $t$ seconds.

Every second he took any piece of the map and tore it into $k$ parts. When he finished, he found $n$ scraps in front of him.

While he was destroying the map, he lost track of time. Now he wants to know how long he tore the map, so he asked you to find $t$.

The first line contains two integers $n$ and $k$ ($1 \le n, k \le 10^9$).

If no suitable $t$ exists, print a single number $-1$. Otherwise, print $t$.