# Divisor Increase

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

There is an integer $k$. You are allowed to add to $k$ any of its divisors not equal to $1$ and $k$. The same operation can be applied to the resulting number and so on. Notice that starting from the number $4$, we can reach any composite number by applying several such operations. For example, the number $24$ can be reached starting from $4$ using $5$ operations: $4→6→8→12→18→24$.

You have to solve a more general problem. Find the minimal number of the described operations necessary to transform $n$ into $m$.

## Input

Each line contains two integers $n$ and $m(4≤n≤m≤10_{5})$.

## Output

For each test case, print in a separate line the minimal number of operations to transform $n$ into $m$. Print $−1$ if $m$ can't be obtained from $n$.

## Examples

Input #1

Answer #1

Submissions 168

Acceptance rate 19%