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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use Math::BigInt;
($a,$b)=split/ /,<>;
$gcd = Math::BigInt::bgcd($a, $b);

for($i=2;$i<=$gcd;$i++){
	if($a%$i==0 && $b%$i==0){
		push @ary,$i;
    }
}
@ary=sort{$b <=> $a}@ary;
for($i=0;$i<=$#ary;$i++){
	$flg=0;
	for($j=$i;$j<=$#ary;$j++){
    	if($j > $i){
    		if($ary[$i] % $ary[$j]==0){
            	$flg=1;
            }
        }
    }
    if($flg==0){
    	$cnt++;
    }
}
print $cnt+1;