P4988 Rearranging DL.

The level order in Dancing Line always feels kind of random.

On this day, Umaru set a new rule for the level order in Dancing Line: suppose a certain level is the $n$-th released level, then its position $a_n$ satisfies $a_{n+1}=(\sqrt[k]{a_n-n}+2)^k+n+1$, and the first released level is always placed first, i.e., $a_1=2$. But this clearly causes a problem: many positions will be empty levels. So Umaru added another restriction: adjust $k$ so that the $n$-th level satisfies $a_n \equiv b\pmod{m}$. Now Umaru gives $n,m,b$, and you need to find the smallest **integer** $k$ that satisfies the condition.

The first line contains three numbers $n,m,b$.

Output one number, representing the smallest $k$; if the smallest $k$ does not exist, output `INF`.

For $30\%$ of the testdata, $n\le 100$, $0\le b