### Problem Statement

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 will solve a more general problem. Given ints N and M, return the minimal number of the described operations necessary to transform N into M. Return -1 if M can't be obtained from N.

### Definition

 Class: DivisorInc Method: countOperations Parameters: int, int Returns: int Method signature: int countOperations(int N, int M) (be sure your method is public)

### Constraints

-N will be between 4 and 100000, inclusive.
-M will be between N and 100000, inclusive.

### Examples

0)

 `4` `24`
`Returns: 5`
 The example from the problem statement.
1)

 `4` `576`
`Returns: 14`
 The shortest order of operations is: 4->6->8->12->18->27->36->54->81->108->162->243->324->432->576.
2)

 `8748` `83462`
`Returns: 10`
 The shortest order of operations is: 8748->13122->19683->26244->39366->59049->78732->83106->83448->83460->83462.
3)

 `235` `98234`
`Returns: 21`
4)

 `4` `99991`
`Returns: -1`
 The number 99991 can't be obtained because it is prime.
5)

 `82736` `82736`
`Returns: 0`
 We don't need any operations. N and M are already equal.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6186

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=9823&pm=6186

Andrew_Lazarev

#### Testers:

PabloGilberto , brett1479 , legakis , Olexiy

#### Problem categories:

Graph Theory, Math