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: Wrong Answer)

my ($A, $B) = map {$_ + 0} split(/ /o, <STDIN>);
my $t = &mygcd($A, $B);
my %h;
foreach my $v ( &factorization($t) ){
  $h{$v} = 1;
}
my $n = keys %h;
$n++;
print $n;

sub mygcd($$) {
  my ($a, $b) = @_;
  while ($b) {
    my $r = $a % $b;
    $a = $b;
    $b = $r;
  }
  return $a;
}
sub factorization {
    my $arg = shift;
    for my $i (2 .. $arg - 1) {
      if ($arg % $i == 0) {
        return ($i, &factorization($arg / $i));
      }
    }
    return $arg;
}