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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program sample
    implicit none
    character(100)::s,t
    integer(8) :: i,j,k,m,n,ans
    integer(8)::a,b,c,d
    integer(8),allocatable::y(:)
  
    read(*,*) a,b
    c=min(a,b)
    d=max(a,b)
    a=c
    b=d
    if(a==1)then
        write(*,*)1
        stop
    end if
    do i=1,1000
        c=mod(b,a)
        b=a
        a=c
        if(a==0)then
            exit
        end if
    end do
    a=b
    
    c=0
    ans=1
    d=int(sqrt(real(b)))
    do i=2,d+1
        c=0
        do j=1,100
            if(mod(a,i)==0)then
                a=a/i
                if(c==0)then
                    c=1
                    ans=ans+1
                end if
            else
                exit
            end if
        end do
        if(a==1)then
            exit
        end if
    end do
    write(*,*)ans


   
    stop
end program sample