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.split.map(&:to_i)
#A,B=10**12, 10**12-100


if A == B
  ans=0
  n = Math.sqrt(A).to_i
  (1..n).each do |i|
    if A % i == 0
      ans+=1
    end
  end
  p ans
  
else
  n = A.gcd(B)
  kou=[]
  (1..n).each do |i|
    if A%i == 0 && B%i == 0
      kou << i
    end
  end
  ans=[]
  size=kou.size
  size.times do |i|
    flag=true
    size.times do |j|
      next if i == j
      next if j == 0
      if kou[i]%kou[j] == 0
        flag=false
      end
    end
    ans << kou[i] if flag
  end
  p ans.size
end