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: Wrong Answer)

<?php
//error_reporting(0);
//$N = trim(fgets(STDIN));
list($A,$B) =  explode(" ",trim(fgets(STDIN)));
//$A = explode(" ",trim(fgets(STDIN)));

$x = gcd($A,$B);
if ($x==1) {
  printf("1\n");
  exit;
}
$a = array_unique(prime_factors($x));
$a[]=$x;

$r=0;
foreach($a as $v) {
  if (is_prime($v)) {
   $r++;
  }
}
printf("%d\n",$r+1);

function gcd($a,$b) {
  if ($b == 0) return $a;
  return gcd($b,$a%$b);
}
function lcm($a,$b) {
  $l = gcd($a,$b);
  return $a / $l * $b;
}

function prime_factors(int $n) {
    $i = 2;
    $factors = [];
    while ($i * $i <= $n) {
        if ($n % $i) $i += 1;
        else {
            $n /= $i;
            $factors[] = $i;
        }
    }
    if ($n > 1) $factors[] = $n;
    return $factors;
}

function is_prime(int $n) : bool {
    $r = true;
    if ($n < 2) $r = false;
    elseif ($n == 2 || $n == 3 || $n == 5) $r = true;
    elseif ($n & 1 == 0) $r = false;
    elseif ($n % 2 == 0 || $n % 3 == 0 || $n % 5 == 0) $r = false;
    else {
        $f = true;
        $v = 7;
        $m = intval($n ** 0.5) + 1;
        while ($v < $m) {
            if ($n % $v == 0) {
                $r = false;
                break;
            }
            $v += $f ? 4 : 2;
            $f = !$f;
        }
    }
    return $r;
}