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: Time Limit Exceeded)

def my_gcd(x, y):
    if x >= y:
        m = x
        n = y
    else:
        m = y
        n = x
    r = m % n
    while r:
        m = n
        n = r
        r = m % n
    return n

def _is_prime(n):
    for i in range(n - 1):
        if (i + 1) ** (n - 1) % n != 1:
            return False
    return True

a, b = map(int, input().split())
g = my_gcd(a, b)
count = 1
num = g
d = 2
while num > 1:
    if _is_prime(d):
        flag = True
        while not num % d:
            if flag:
                count += 1
                num = num // d
                flag = False
            else:
                num = num // d
        d += 1
    else:
        d += 1
print(count)