#P1141A. Game 23
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ID: 4683
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Game 23
No submission language available for this problem.
Description
Polycarp plays "Game 23". Initially he has a number $n$ and his goal is to transform it to $m$. In one move, he can multiply $n$ by $2$ or multiply $n$ by $3$. He can perform any number of moves.
Print the number of moves needed to transform $n$ to $m$. Print -1 if it is impossible to do so.
It is easy to prove that any way to transform $n$ to $m$ contains the same number of moves (i.e. number of moves doesn't depend on the way of transformation).
The only line of the input contains two integers $n$ and $m$ ($1 \le n \le m \le 5\cdot10^8$).
Print the number of moves to transform $n$ to $m$, or -1 if there is no solution.
Input
The only line of the input contains two integers $n$ and $m$ ($1 \le n \le m \le 5\cdot10^8$).
Output
Print the number of moves to transform $n$ to $m$, or -1 if there is no solution.
Samples
120 51840
7
42 42
0
48 72
-1
Note
In the first example, the possible sequence of moves is: $120 \rightarrow 240 \rightarrow 720 \rightarrow 1440 \rightarrow 4320 \rightarrow 12960 \rightarrow 25920 \rightarrow 51840.$ The are $7$ steps in total.
In the second example, no moves are needed. Thus, the answer is $0$.
In the third example, it is impossible to transform $48$ to $72$.