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: Accepted)

def my_gcd(a, b)
  while b!=0 do
    c=a%b
    a=b
    b=c
  end
  return a
end

def my_soinsu_bunkai(n)
  arr=[]
  arr<<1
  i = 2

  while (i*i)<=n
    #puts "now n = #{n}, arr = #{arr}"
    if n%i==0
      arr<<i
      while n%i==0 do
        n/=i
      end
    else
      i+=1
    end
  end
  #puts i
  #puts n 
  if n!=1
    arr<<n
  end
  return arr
end

a,b = gets.chomp.split(" ").map{|i|i = i.to_i}

g = my_gcd(a,b)
#puts "my_gcd(#{a},#{b}) = #{g}"
array = my_soinsu_bunkai(g)
#pp array
puts array.length
=begin
(Math.sqrt(g).to_i).times{|i|
  n = i+1
  if 
}
=end