CF1141A.Game 23

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题目描述

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).

输入格式

The only line of the input contains two integers $n$ and $m$ ( $1 \le n \le m \le 5\cdot10^8$ ).

输出格式

Print the number of moves to transform $n$ to $m$ , or -1 if there is no solution.

输入输出样例

输入#1
```
120 51840
```
输出#1
```
7
```
输入#2
```
42 42
```
输出#2
```
0
```
输入#3
```
48 72
```
输出#3
```
-1
```

说明/提示

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 $72$ .

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