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: Accepted)

<?php


fscanf(STDIN, "%d%d", $a, $b);
$min = min($a, $b);
if($min != $a){
    list($a, $b) = [$b, $a];
}
$max = (int)(sqrt($b)) + 1;
$ans = 1;
if($a % 2 == 0 && $b % 2 == 0){
    while($a % 2 == 0){
        $a = $a / 2;
    }
    $ans++;
}
for($i = 3; $i<=$max; $i=$i+2){
    if($a < $i){
        break;
    }
    if($a % $i == 0 && $b % $i ==0){
        while($a % $i == 0){
            $a = $a / $i;
        }
        $ans++;
    }
}

if(gcd($a, $b) > $max){
    $ans++;
}
echo $ans;
exit;


function gcd($m, $n){

    while($n !== 0){
        $tmp_n = $n;
        $n = $m % $n;
        $m = $tmp_n;
    }
    return $m;
}