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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use List::Util 'min';
($x,$y)=split(/ /,<>);
for $i (1 .. min($x,$y)){
 push(@c,$i) if(($x % $i == 0) and ($y % $i ==0));
}
@r = ();
for (@c){
 if($_ == 1){
  push(@r,$_);
  next;
 }
 $f = 0;
 if($_ != 2){
  if ($_ % 2 == 0){
   $f = 1;
  }else{
   for ($i=3;$i<=$_/$i;$i+=2){
    if($_ % $i == 0){
     $f = 1;
     last;
    }
   }
  }
 }
 push(@r,$_) if($f == 0);
}

print scalar(@r) . "\n";