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)

a, b = map(int, input().split())

def gcd(x, y):
    if x < y: x, y = y, x
    while y != 0:
        x, y = y, x % y
    return x

gcd_ab = gcd(a, b)
if gcd_ab == 1:
    print(1)
    exit()

def get_divisor(n):
    divisor = {}
    if n % 2 == 0:
        divisor[2] = 1
        # if 2 in divisor:
        #     divisor[2] += 1
        # else:
        #     divisor[2] = 1
        # n //= 2

    i = 3
    while i <= n:
        while n % i == 0:
            if i in divisor:
                divisor[i] += 1
            else:
                divisor[i] = 1
            n //= i
        i += 2
    return divisor

divisor = get_divisor(gcd_ab)
print(len(divisor)+1)