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: Runtime Error)

<?php

$a_b = explode(" ", (trim(fgets(STDIN))));

$a_dividor = [(int)$a_b[0], 1];

$b_dividor = [(int)$a_b[1], 1];

$dividor = [1];

for ($i = floor($a_b[0]/2); $i >= 0; $i--) {
     if($a_b[0] % $i === 0) {
        if(in_array($i, $a_dividor)){
            break;
        }
        
        $a_dividor[] = (int)$i;
        $a_dividor[] = (int)$a_b[0] / $i;
     }
}

for ($i = floor($a_b[1]/2); $i >= 0; $i--) {
     if($a_b[1] % $i === 0) {
        if(in_array($i, $b_dividor)){
            break;
        }
        
        if(in_array($i, $a_dividor)) {
            $dividor[] = (int)$i;
        }
        
        if(in_array($a_b[1] / $i, $a_dividor)) {
            $dividor[] = (int)$a_b[1] / $i;
        }
        
        
        $b_dividor[] = (int)$i;
        $b_dividor[] = (int)$a_b[1] / $i;
     }
}

$count = 0;
$memo = [];
for ($i = 0; $i < count($dividor); $i++) {
     for ($j = 0; $j < count($dividor); $j++) {
         
          if(isset($memo[$i][$j])) continue;
          if($i == $j) continue;
                   
          if(is_prime($dividor[$i]) && is_prime($dividor[$j])) {
                $count++;
          }
          $memo[$i][$j] = true;
          $memo[$j][$i] = true;
          
     }
}

echo $count;

function is_prime($number){ 
    if ($number == 1) 
    return 0; 
    for ($i = 2; $i <= $number/2; $i++){ 
        if ($number % $i == 0) 
            return 0; 
    } 
    return 1; 
}