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 Python (3.4.3) (judge verdict: Runtime Error)

from fractions import gcd
import math
import numpy as np
N = list(map(int, input().split()))
g = gcd(N[0], N[1])
max_prime = g + 2
primes = np.ones(max_prime)
#print(g+1, primes.shape)
primes[0:2] = 0
#print(primes)
for i in range(2, int(np.sqrt(max_prime))+2):
  if i * 2 < max_prime:
    primes[i*2::i] = 0
    #print(i, primes)
    
primes = np.arange(max_prime)[primes == 1]
#print(primes)

factor = []
for i in primes:
  if g % i == 0:
    #print(g)
    factor.append(i)

#print(g, factor)
print(len(factor) + 1)