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   Problem Statement  

 Problem Statement for BigFatInteger

Problem Statement

    

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Lun the dog loves very large integers. Her favorite is AB (A to the power of B).



She has an integer variable X. Initially, the value of X is set to 1. She can perform the following two kinds of operations in any order, any number of times.
  • Operation 1: choose a prime number p, then multiply X by p.
  • Operation 2: choose a positive divisor d of the value of X at that point, then multiply X by d.




You are given two ints A and B. Return the minimum number of operations Lun needs to perform in order to obtain X = AB from the initial state X = 1.
 

Definition

    
Class:BigFatInteger
Method:minOperations
Parameters:int, int
Returns:int
Method signature:int minOperations(int A, int B)
(be sure your method is public)
    
 

Constraints

-A will be between 2 and 1,000,000 (106), inclusive.
-B will be between 1 and 1,000,000 (106), inclusive.
 

Examples

0)
    
6
1
Returns: 2
Here, AB = 61 = 6. Here is one of the optimal sequences of operations:
  1. Perform operation 1 by choosing p=2. X is now 1*2 = 2.
  2. Perform operation 1 by choosing p=3. X is now 2*3 = 6.
1)
    
162
1
Returns: 4
One of the optimal sequences of operations:
  1. Perform operation 1 by choosing p=3. X is now 1*3 = 3.
  2. Perform operation 1 by choosing p=3. X is now 3*3 = 9.
  3. Perform operation 2 by choosing d=9. X is now 9*9 = 81.
  4. Perform operation 1 by choosing p=2. X is now 81*2 = 162.
2)
    
999983
9
Returns: 5
Here, A is prime. One of the optimal sequences of operations:
  1. Perform operation 1 by choosing p=A. X is now A.
  2. Perform operation 1 by choosing p=A. X is now A2.
  3. Perform operation 1 by choosing p=A. X is now A3.
  4. Perform operation 2 by choosing d=A3. X is now A6.
  5. Perform operation 2 by choosing d=A3. X is now A9.
3)
    
360
8
Returns: 8

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This problem was used for:
       Single Round Match 599 Round 1 - Division I, Level One