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: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d %d", $a, $b);
function gcd($x,$y){
    if($y == 0) {
        return $x;
    } else {
        return gcd($y, $x%$y);
    }
}
$gcd = gcd($a, $b);

$max = floor(sqrt($gcd));
$lists = array();
$primeLists = array();

for($i = 2; $i <= $gcd; $i++) {
    $lists[$i] = $i; // 振るいをかけるリストの作成
}

while ($val = array_shift($lists)) {
    $primeLists[] = $val;
    if($val > $max) { // $valが$gcdの平方根に達したら終了
    break;
    }
    foreach($lists as $key2 => $val2) {
        if($val2 % $val === 0) {
            unset($lists[$key2]);
        }
    }
}
$primeLists = array_merge($primeLists, $lists);
$ans = array();
foreach($primeLists as $value) {
    if($gcd % $value === 0) {
        $ans[] = $value;
    }
}
echo count($ans) + 1;