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: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d %d", $a, $b);
$min = min($a, $b);
$cmn = [];
for ($i = 1; $i <= $min; $i++) {
  if ($a % $i == 0 && $b % $i == 0) $cmn[] = $i;
}
$prm = [];
foreach ($cmn as $n) {
  foreach ($prm as $p) {
    if (!isPrm($p, $n)) continue 2;
  }
  $prm[] = $n;
}
echo count($prm);
function isPrm($a, $b) {
  if ($a == 1) return true;
  for ($i = 2; $i <= $a; $i++) {
    if ($a % $i == 0 && $b % $i == 0) return false;
  }
  return true;
}