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.chop.split.map(&:to_i)

#a==bだけだめ！！！
if a == b
    ans = []

    #aのほうが小さいとする。
    root_a = a**(1/2.0)
    root_a = root_a.floor.to_i

    ans = []

    for index in 1..root_a
      if a % index == 0
        ans << index
        ans << a / index
      end
    end

else


  if a > b
    a, b = b, a
  end

  #aのほうが小さいとする。
  root_a = a**(1/2.0)
  root_a = root_a.floor.to_i

  ans = []

  for index in 1..root_a
    if b % index == 0 && a % index == 0
      ans << index
      ans << a / index
      ans << b / index
    end
  end

end

answer = 1

ans.each{ |i|
  if i == 1
    next
  end
  flag = 1

  #あるiに対して全てを割ってみる
  ans.each{ |j|
    if j == 1 || i == j
      next
    end

    if i % j == 0
      flag = 0
      break
    end
   }

   if flag == 1
     answer += 1
   end
 }

 print answer