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)

import random

def gcd(a,b):
        if b == 0:
                return a
        else:
                return gcd(b , a%b) 
def is_prime(q,k=50):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1

    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1:
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

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

c = 1
m = gcd(a,b)

i = 1
while i * i <=m:
        if a%i == 0 and b%i == 0:
                if is_prime(i):
                        c+=1
                if is_prime(m//i):
                        c+=1
        i+=1
print(c)