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)

require 'prime'

def gcds(nums)
  d = 0
  nums.each{ |num| d = num.gcd(d) }
  d
end

a, b = gets.split(" ").map(&:to_i)
a_result = []
a_result << 1
b_result = []
b_result << 1

a_array = []
a.prime_division.each do |a, b|
  b.times do
    a_array << a
  end
end

(1..a_array.length).each do |i|
  a_array.combination(i) do |array|
    a_result << array.inject{ |a, b| a *= b }
  end
end

b_array = []
b.prime_division.each do |a, b|
  b.times do
    b_array << a
  end
end

(1..b_array.length).each do |i|
  b_array.combination(i) do |array|
    b_result << array.inject{ |a, b| a *= b }
  end
end

result = a_result.uniq & b_result.uniq

result.length.downto(1) do |i|
  flag = true
  if i == 0
    break
  end

  result.combination(i) do |array|

    array.length.downto(1) do |j|
      if j == 0
        break
      end

      array.combination(2) do |a, b|
        unless a.gcd(b) == 1
          flag = false
        end
      end

      if flag
        puts array.length
        exit
      end
    end
  end
end

puts 0