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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# 1. 最大公約数を求める(ユークリッドの互除法)
# 2. 最大公約数を素因数分解する。
# 3. 2.の結果に含まれる素数＋１が答え

import itertools
from fractions import gcd

def main():
  a, b = map(int, input().split())
  c = gcd(a,b)
  
  fac = [1]
  fac = facto(c)
  # print(fac)
  print(len(fac))  
  
def facto(n):
  if n == 1:
    return [1]
  elif n == 2:
    return[1, 2]
  elif n % 2 == 0:
    fac = [1, 2]
    while n % 2 == 0:
      n = n // 2
  else:
    fac = [1]
  
  max_n = int(n ** 0.5 + 2)
  
  is_prime = [True for x in range(max_n)]
  for cursor in range(3, max_n, 2):
    if is_prime[cursor]:
      if n % cursor == 0:
        fac.append(cursor)
        while n % cursor == 0:
          n = n // cursor
        if n == 1:
          break
      for i in range(cursor, max_n, cursor):
        is_prime[i] = False
  else:
    fac.append(n)
    
  return fac
  

if __name__ == "__main__":
  main()