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: Accepted)

from collections import defaultdict
import math


def make_prime_list(num):
    if num < 2:
        return []
    prime_list = [i for i in range(num + 1)]
    prime_list[1] = 0
    num_sqrt = math.sqrt(num)
    for prime in prime_list:
        if prime == 0:
            continue
        if prime > num_sqrt:
            break
        for non_prime in range(2 * prime, num, prime):
            prime_list[non_prime] = 0
    return [prime for prime in prime_list if prime != 0]


def prime_factorization(num):
    if num <= 1:
        return {}
    else:
        num_sqrt = math.floor(math.sqrt(num))
        prime_list = make_prime_list(num_sqrt)
        dict_counter = defaultdict(int)
        for prime in prime_list:
            while num % prime == 0:
                dict_counter[prime] += 1
                num //= prime
        if num != 1:
            dict_counter[num] += 1
        dict_counter = dict(dict_counter)
        return dict_counter


a, b = map(int, input().split())
buf = a
while buf!=0:
    a,b=b,buf
    buf=a%b
print(len(prime_factorization(b))+1)