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
// $n = (int)trim(fgets(STDIN));
$input = explode(' ', trim(fgets(STDIN)));

$a = (int)$input[0];
$b = (int)$input[1];

// 最大公約数
$gcd = gcd($a, $b);

// 1
$cnt = 1;
if ($gcd === 1) {
	echo $cnt;
	exit();
}
// 2
$tmp = $gcd;
$flg = false;
while ($tmp % 2 === 0) {
	$tmp = (int)floor($tmp/2);
	$flg = true;
}
if ($flg) {
	$cnt += 1;
}
// 3以上
$max = (int)ceil(sqrt($gcd));
for ($i=3; $i <= $max; $i+=2) { 
	$flg = false;
	while ($tmp % $i === 0) {
		$tmp = (int)floor($tmp/$i);
		$flg = true;
	}
	if ($flg) {
		$cnt += 1;
	}
}
if ($cnt === 1 ) {
	$cnt += 1;
}
echo $cnt;


function gcd($m,$n){
	if ($m === $n) {
		return $m;
	}
	$large = max($m,$n);
	$small = min($m,$n);
	$q = $large % $small;
	if ($q === 0) {
		return $small;
	}else{
		return gcd($small, $q);
	}
}
// 素数判定
// function sieve($n){
// 	$list = range(2, $n);
// 	$result = [1];
// 	for ($i=1; $i < $n; $i++) { 
// 		// echo implode(' ', $list) , PHP_EOL;
// 		$tmp_list = [];
// 		$target = array_shift($list);
// 		if (empty($target)) {
// 			break;
// 		}
// 		$result[] = $target;
// 		foreach ($list as $v) {
// 			if ($v % $target !== 0) {
// 				$tmp_list[] = $v;
// 			}
// 		}
// 		$list = $tmp_list;
// 	}
// 	return $result;
// }