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 PHP (5.6.30) (judge verdict: Runtime Error)

<?php

$input_line = "";
while (($buffer = fgets(STDIN)) !== false) {
    $input_line.= $buffer;
}

$input_line = trim($input_line);
$input_array =  explode("\n", $input_line);
preg_match("/([0-9]+) ([0-9]+)/", array_shift($input_array), $two_nums);

$max_common_divisor = euclidean($two_nums[1], $two_nums[2]);
$count = 1;
$now = 1;
while (($now = gmp_nextprime($now)) <= $max_common_divisor){
    if ($two_nums[1] % $now == 0 && $two_nums[2] % $now == 0) {
        $count++;
    }
}

echo $count;

function euclidean($x, $y)
{
    if ($y == 0) {
        return $x;
    }
    return euclidean($y, (int)$x % $y);
}