Problem:
Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  fscanf(STDIN,"%d %d",$a,$b) ;
$cc=[];
$cd=[];
$ans=1;
$c = min($a,$b);
$d = max($a,$b);
if($c%2==0){
$cc[]=2;
}
for($i=3;$i<$c/2;$i+=2){
if($c%$i==0){
  $cc[] = $i ;
}}
foreach($cc as $v){
if($d%$v==0){
  $cd[] = $v ;
}}
foreach($cd as $val){
  if($val == 2){
    ++$ans;
    continue;
  } 
  $inc = true ;
  for($i=3;$i<sqrt($val)+1;$i+=2){
    if($val%$i==0){
      $inc = false ;
    break ;
    }
  }
 if($inc){ 
  ++$ans ;
   }
}

echo $ans ;