CF1141A Game 23

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.

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 $ .