Game 23

1000ms

262144K

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).

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.

Sample Input:

120 51840

Sample Output:

Sample Input:

42 42

Sample Output:

Sample Input:

48 72

Sample Output:

-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 $$$72$$$.

Informação

Provedor Codeforces

Código CF1141A