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 Ruby (2.3.3) (judge verdict: Wrong Answer)

a,b=gets.chomp.split(" ").map(&:to_i)
r=(a<b) ? a : b
f=a+b-r
divisorList=[]
prime=Array.new((f**0.5).to_i){1}
((r**0.5).to_i+1).times do|i|
  next if i.zero?
  if (a%i).zero? and (b%i).zero?
    divisorList.push(i) 
    divisorList.push(a/i) if i!=a/i and (b% (a/i)).zero?
  end
  next if i==1
  j=2
  if prime[i]==1
    while j*i<=(f**0.5).to_i
      prime[j*i]=0
      j+=1
    end
  end
end
ans=0
divisorList.each do|c|
  ans+=1 if prime[c]==1
end
puts ans