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: Time Limit Exceeded)

# coding: utf-8
class Case04

  def initialize
  end

  def show
    p self.instance_variables
        .map{ |sym| [sym, self.instance_variable_get(sym)] }
        .to_h
  end

  def gcd(x,y)
    if x < y then
      x, y = y, x
    end
    r = x % y
    while r != 0 do
      x = y
      y = r
      r = x % y
    end
    y 
  end

  def prime_dev(x)
    @d = []
    #2.upto(Math.sqrt(x).to_i + 1) do |p|
    2.upto(x) do |p|
        q = 0
      while x % p == 0 do
        q += 1
        x = x / p
      end
      @d << q if q > 0
    end
    # @d.reduce(1) { |r,x| r * (x + 1) } -1
    @d.length + 1
  end
  
  # 実行する
  def execute
    read
    solve
    output
  end

  # 読込
  def read
    @a, @b  = gets.chomp.split.map(&:to_i)
  end

  # 回答
  def solve
    @g = gcd(@a, @b)
    @result = prime_dev(@g)
  end
  
  # 出力
  def output
    puts @result
  end

end

Case04.new.execute if $0 == __FILE__