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
fscanf(STDIN, '%d %d', $a, $b);
$gcd = gcd($a, $b);
$is_prime = is_prime($gcd);
$ans = 1;
for ($i = 2; $i <= $gcd; $i++) {
    if ($a % $i === 0 && $b % $i === 0 && $is_prime[$i]) {
        $ans++;
    }
}
echo $ans.PHP_EOL;

/**
 * エラトステネスのふるい
 * $maxまでの整数が素数かどうかboolを格納した配列を返す
 */
function is_prime($max) {
    $arr = array_fill(0, $max + 1, true);
    $arr[0]  = $arr[1] = false;
    $rmax = floor(sqrt($max));
    for ($i = 2; $i <= $rmax; $i++) {
        for ($j = 2 * $i; $j <= $max; $j += $i) {
            $arr[$j] = false;
        }
    }
    return $arr;
}

// 最大公約数
function gcd($m, $n){
    if($n > $m) list($m, $n) = [$n, $m];
    if ($m % $n === 0) return $n;
    else return gcd($n, $m % $n);
}