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)

def gcd(_x, _y)
  if _x < _y
    _x, _y = _y, _x
  end
  while _y > 0
    r = _x % _y
    _x = _y
    _y = r
  end
  return _x
end

def isprime(_x)

  if _x < 2
    return false
  elsif _x == 2
    return true
  elsif _x % 2 == 0
    return false
  end

  l = Math.sqrt(_x).to_i
  3.step(l, 2) do |i|
    if _x % i == 0
      return false
    end
  end
  return true
end
a, b = gets.chomp.split(' ').map(&:to_i)

# 最大公約数を求める
g = gcd(a, b)

# 最大公約数の約数を求める
cd = [1]
if g > 1
  if g % 2 == 0
    cd.push(2)
  end
  3.step(g, 2) do |i|
   if g % i == 0
     if isprime(i)
       cd.push(i)
     end
   end
  end
end
puts cd.size.to_s