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);

$acd = [];
for ($i = 1; $i <= sqrt($a); ++$i) {
    if ($a % $i === 0) {
        $acd[] = $i;
        $acd[] = $a / $i;
    }
}

$bcd = [];
for ($i = 1; $i <= sqrt($b); ++$i) {
    if ($b % $i === 0) {
        $bcd[] = $i;
        $bcd[] = $b / $i;
    }
}

$cd = array_unique(array_intersect($acd, $bcd));
sort($cd);

$cnt = 0;
foreach ($cd as $val) {
    $flg = true;
    for ($j = 2; $j <= sqrt($val); ++$j) {
        if ($val % $j === 0) {
            $flg = false;
            break;
        }
    }
    $cnt += $flg ? 1 : 0;
}

echo $cnt;